Given that angle A = 30 degrees, side a = 10ft, and side b =
8ft, find the remaining sides and angles of the triangle if they
exist.

Answers

Answer 1

The remaining sides and angles of the triangle are side c ≈ 18.47 ft, angle B ≈ 23.58 degrees, and angle C ≈ 126.42 degrees.

To find the remaining sides and angles of the triangle given that angle A = 30 degrees, side a = 10ft, and side b = 8ft, we need to determine if the given information represents a valid triangle. Since we have one angle and two sides, we can use the Law of Sines.

The Law of Sines states that (a/sinA) = (b/sinB) = (c/sinC), where a, b, and c are the sides of the triangle, and A, B, and C are the corresponding angles.
Step 1: Use the given information to find angle B.
(10/sin(30)) = (8/sinB)
10/sin(30) = 8/sinB
10/0.5 = 8/sinB
20 = 8/sinB
sinB = 8/20
sinB = 0.4
B = arcsin(0.4)
Angle B ≈ 23.58 degrees
Step 2: Find angle C.
Since the sum of angles in a triangle is 180 degrees:
C = 180 - (A + B)
C = 180 - (30 + 23.58)
C ≈ 126.42 degrees
Step 3: Find side c using the Law of Sines.
(10/sin(30)) = (c/sin(126.42))
10/0.5 = c/sin(126.42)
20 = c/sin(126.42)
c ≈ 20 * sin(126.42)
c ≈ 18.47 ft
So, the remaining sides and angles of the triangle are side c ≈ 18.47 ft, angle B ≈ 23.58 degrees, and angle C ≈ 126.42 degrees.

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Related Questions

What is the first step in solving the following system of equations?

3 x + y = 23.
8 x + 2 y = 23.

Answers

Answer:

Solve the first equation for y

Step-by-step explanation:

the two congruent sides of an isosceles triangle form the

Answers

In an isosceles triangle, the two https://brainly.com/question/28412104 form the two equal angles opposite those sides.

An isosceles triangle is a type of triangle that has two sides of equal length. The two congruent sides are referred to as the legs of the triangle, while the remaining side is known as the base. The key property of an isosceles triangle is that the angles opposite the congruent sides are also equal. This means that the triangle has two equal angles formed by the congruent sides and a third angle formed by the base.

To understand why the congruent sides form equal angles, consider the following: When two sides of a triangle are equal in length, it implies that the opposite angles they form are also equal. This is known as the Isosceles Triangle Theorem. In an isosceles triangle, the two congruent sides are equal in length, which means the angles opposite those sides must also be equal. Therefore, the two congruent sides of an isosceles triangle form the two equal angles opposite them.

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how do you solve when the percent is greater than 100

Answers

Answer:

Below

Step-by-step explanation:

100 % = 1.00 in decimal

125% = 1.25 in decimal

EXAMPLE:

125% 0f 12   =   1.25 * 12 = 15  

Sherri and Deion both have square posters. Sherri's poster has an area of 49 square inche. If Deion's poster has an area that is 4 square inches less than Sherri's poster, what are the side length of Sherri and Deion's posters


A. sherri's poster: 7 inches; Deions poster:5 inches

B. Sherri 7 inches; Deion: 45 squared inches

C. sherri: 45 squared inches; Deion: 5 inches

D. Sherri: 45 squared; Deion: 7 inches​

Sherri and Deion both have square posters. Sherri's poster has an area of 49 square inche. If Deion's

Answers

Answer: i think its B

Step-by-step explanation:

John took 8 hours to drive 320 miles. At this same rate, how far will he travel in 16 hours?

Answers

Answer:

640 Miles

Step-by-step explanation:

The volume of a cylinder is 128(pi)cm^3. The height of the cylinder is twice the length of the radius. Find the measure of the radius.

Answers

Answer:

128/2 = 64 which gives you the height

sq root 64 = 8 which gives you the diameter

8/2= 4cm which is the radius (answer)

what is the quotient of 6x^3+2x-x/x where x≠0

Answers

Answer:

6\(x^{2}\) + 1

Step-by-step explanation:

\(\frac{6x^{3}+ 2x-x }{x}\)   combine 2x -x = x

\(\frac{6x^{3} + x}{x}\)

\(\frac{x(6x^{2} + 1) }{x}\)  the x's cancel out

6\(x^{2}\) + 1

how many 6-person lineups can be formed from a volleyball roster of 12 players, assuming every player can play any position?

Answers

Answer:2

Step-by-step explanation:

12/6=2

There are 924 possible outcomes 6-person lineups that can be formed from a volleyball roster of 12 players, assuming every player can play any position.

To answer your question, we can use the combination formula which is nCr = n!/(r!(n-r)!), where n is the total number of players in the roster and r is the number of players we want to choose for the lineup. In this case, we want to choose 6 players for the lineup out of 12 players in the roster. So, the formula becomes 12C6 = 12!/(6!(12-6)!) = 924. Therefore, there are 924 possible 6-person lineups that can be formed from the volleyball roster of 12 players, assuming every player can play any position.

To form a 6-person lineup from a 12-player volleyball roster, you can use the concept of combinations. Combinations are used to find the number of ways to choose items from a larger set without considering the order of the items. In this case, you need to choose 6 players from a set of 12. The formula for combinations is:

C(n, k) = n! / (k!(n-k)!)

where C(n, k) is the number of combinations, n is the total number of items, k is the number of items to choose, and ! denotes the factorial of a number. Plugging in the values for your question:

C(12, 6) = 12! / (6!(12-6)!)

C(12, 6) = 12! / (6!6!)

C(12, 6) = 924

So, there are 924 possible outcomes 6-person lineups that can be formed from a volleyball roster of 12 players, assuming every player can play any position.

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What is the probability that either event will occur?
15
A
17
B
2
P(A or B) = P(A) + P(B)
P(A or B) = [?]

Answers

The probability that either event will occur is 0.83

What is the probability that either event will occur?

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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What is the probability that either event will occur?15A17B2P(A or B) = P(A) + P(B)P(A or B) = [?]

given the functions f(x)=3/2 and g(x)=7/3x-8/3, find(f*g)(x)

Answers

Answer:

pagal man

Step-by-step explanation:

tumko Answer Nahi Aata Padhte Likhte Nahi hoo kya

Calculate the cost (in cents) of using a 200 watt television for 30 days if turned on 2 hours per day and if electricity costs 10 cents per kilowatt-hour

Answers

Answer:

The awnser to this equation is 120 cents

The cost of using a 200-watt television for 30 days, turned on for 2 hours per day, would be $1.20.  

To calculate the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour, we need to find the total energy consumption and then multiply it by the cost per kilowatt-hour.

First, let's find the total energy consumption:


1. Daily energy usage: 200 watts * 2 hours = 400 watt-hours
2. Monthly energy usage: 400 watt-hours * 30 days = 12,000 watt-hours

Now, we need to convert watt-hours to kilowatt-hours:
3. Monthly energy usage in kilowatt-hours: 12,000 watt-hours / 1,000 = 12 kWh

Finally, let's calculate the cost:
4. Cost of using the television for 30 days: 12 kWh * 10 cents per kWh = 120 cents

So, the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour is 120 cents.

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Which ratios correctly compare bananas to apples, as
shown in the image? Check all that apply.

Answers

Answer:

where's the picture bro?

Step-by-step explanation:

Answer:

b,c,d- 1:6, one to six, 1/6

Step-by-step explanation:

on edg. I did it and got it right.

If p and q are remainders when the polynomials

If p and q are remainders when the polynomials

Answers

Answer:

Step-by-step explanation:

I wanna be in a gc someone add me to one

Sc-maddison_camp20

Ig- mads_070

Answers

20 words be annoying

find an equation of the tangent plane to the given parametric surface at the specified point. x=u v, y=3u^2, z=u-v

Answers

Therefore, the equation of the tangent plane to the given parametric surface at the specified point is: v0(x - x0) + u0(y - y0) + 6u0(z - z0) + (1)(0) + (-1)(1) = 0.

To find the equation of the tangent plane to the parametric surface at the specified point, we need to find the normal vector to the surface at that point. The normal vector is given by the cross product of the partial derivatives of the surface equations with respect to u and v.

The surface is defined by the parametric equations:

x = u*v

y = 3u^2

z = u - v

Taking the partial derivatives:

∂x/∂u = v

∂x/∂v = u

∂y/∂u = 6u

∂y/∂v = 0

∂z/∂u = 1

∂z/∂v = -1

Taking the cross product of the partial derivatives:

N = (∂x/∂u, ∂x/∂v, ∂y/∂u, ∂y/∂v, ∂z/∂u, ∂z/∂v)

= (v, u, 6u, 0, 1, -1)

At the specified point, let's say u = u0 and v = v0. Plugging these values into the normal vector, we have:

N(u0, v0) = (v0, u0, 6u0, 0, 1, -1)

The equation of the tangent plane can be written as:

(v0, u0, 6u0, 0, 1, -1) · (x - x0, y - y0, z - z0) = 0

Where (x0, y0, z0) is the coordinates of the specified point on the surface.

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Find The slope between this two points:
(5,9),(-2,8)

Answers

Answer:

\( \boxed{\tt \: SLOPE= \cfrac{1}{7}} \)

OR

\(\boxed{ \tt\: SLOPE = 0.142}\)

Step-by-step explanation:

Given:

Two points, i.e.

\( \tt \: (5,9),(-2,8)\)

To Find:

The slope between the two given points.

Solution:

To Find out the slope between two points,we will use the formula of Slope, i.e. :

\( \boxed{\rm \: m = \cfrac{y_ 2 - y_ 1}{x_2 - x_ 1}} \)

According to the Question,

\( \rightarrow \: \rm \: y_2 = 8\)

\(\rightarrow \: \rm \: y_1 = 9\)

\(\rightarrow \: \rm \: x_2 = - 2\)

\(\rightarrow \: \rm \: x_1 = 5\)

Now Substitute the values on the formulae of slope and then Simplify using PEMDAS rule :

\( \rm \: \longrightarrow Slope = \cfrac{8 - 9}{ - 2 - 5} \)

\( \rm \: \longrightarrow Slope = \cfrac{ - 1}{ - 2 - 5} \)

\( \rm \: \longrightarrow Slope = \cfrac{ \cancel- 1}{ \cancel- 7} \)

\( \rm \: \longrightarrow Slope = \cfrac{1}{7} \)

In Decimal,

\( \rm \: \longrightarrow Slope =0.142\)

Hence, the slope between the two given points would be \( 1/7 \) or \( 0.142 \).

\( \rule{225pt}{2pt}\)

I hope this helps!

Have a nice day! :)

Note:

SLOPE is usually denoted as \( m. \)

Find The slope between this two points:(5,9),(-2,8)

Answer:

The slope is 1/7.

Step-by-step explanation:

Use the slope formula.

Slope:

\(\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}\)

y2=8y1=9x2=(-2)x1=5

Rewrite the problem down.

\(\sf{\dfrac{8-9}{(-2)-5}=\dfrac{-1}{-7}=\boxed{\sf{\dfrac{1}{7}}}\)

Dividing is another option.

1/7=0.142.

Therefore, the slope is 1/7, which is our answer.

I hope this helps! Let me know if you have any questions.

What are the slope and y-intercept of 25x - 20y = 100

Answers

What are the slope and y-intercept of

25x - 20y = 100

-20y = 100 - 25x

20y = 25x - 100 (dividing by 20)

y= (25/20)x - 5

y= (5/4)x - 5

So, the slope is 5/4 and the y-intercept is 5.

Factor 403 – 102O 2x (2x - 5)O 2. (x - 5)O 23 (223 – 10)O x (x2 – 10x)

Factor 403 102O 2x (2x - 5)O 2. (x - 5)O 23 (223 10)O x (x2 10x)

Answers

We are asked to factor out the expression:

4 x^3 - 10 x

So we extract a factor of "2" from the numerical factors "4" and "10", and also a factor of "x" from each term,leading to:

2 x ( 2 x^2 - 5)

Therefore, please select the first answer option they give you in the list.

Please help me (picture)

Please help me (picture)

Answers

Answer:the answer is c

Step-by-step explanation:

I need help how do I do this.

What is a number that when you multiply it by 4 and add 15 to the product, you get 79?​

Answers

X*4+15=79
X=(79-15)/4
X=16

Answer:16 multiply by 4 = 64 +15= 79

Step-by-step explanation:

which table of ordered pairs matches the question?​

Answers

Answer:

Can you please tell us the question?

Step-by-step explanation:

45 miles per hour What is its rate in feet per second?

Answers

1 mile = 5,280 feet.

45 miles x 5,280 feet = 237,600 total feet.

1 hour = 3600 seconds

237,600/3600 = 66 feet per second.

Answer:

66 feet per second...I think

Step-by-step explanation:

bob thinks the inverse of y=2x-5 is y =5x-2 identify his error and find the correct inverse

Answers

Answer:

yea he is wrong

Step-by-step explanation:

He is wrong because you cant not just switch the variable. If you move the variable the value will change.

Help with a correct answer:

Help with a correct answer:

Answers

Answer:

23 and 31

Step-by-step explanation:

substitute x = 2 into f(x) and x = 4 into g(x)

f(2) = 2(2) - 3 = 4 - 3 = 1

g(4) = 5(4) + 2 = 20 + 2 = 22

Then

f(2) + g(4) = 1 + 22 = 23

----------------------------------------------

substitute x = 8 into f(x) and x = 2 into g(x)

f(8) = 5(8) - 3 = 40 - 3 = 37

g(2) = 3(2) = 6

Then

f(8) - g(2) = 37 - 6 = 31

Let A = {2,4,6,8,10,12} B = {3,6,9,12,15,18} C = {0,6,12,18} Find C-A. none of the choices {2,3,4,6,8,9,10,12} O {2,4,8,10) {0,18}

Answers

the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

To find the set difference C - A, we need to remove all elements from A that are also present in C. Let's examine the sets:

C = {0, 6, 12, 18}

A = {2, 4, 6, 8, 10, 12}

We compare each element of A with the elements of C. If an element from A is found in C, we exclude it from the result. After the comparison, we find that the elements 2, 4, 8, 10 are not present in C.

Thus, the set difference C - A is {0, 18}, as these are the elements that remain in C after removing the common elements with A.

Therefore, the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

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Find F(s) L{t 14 e −6t }

Answers

To find the Laplace transform of the function f(t) = t^14 * e^(-6t), denoted as L{t^14 * e^(-6t)}, we can use the standard Laplace transform formulas. The Laplace transform of t^n, where n is a positive integer, is given by:

L{t^n} = n! / s^(n+1)

The Laplace transform of e^(at), where a is a constant, is given by:

L{e^(at)} = 1 / (s - a)

Using these formulas, we can calculate the Laplace transform of f(t):

L{t^14 * e^(-6t)} = L{t^14} * L{e^(-6t)}

Applying the formula for t^14 and e^(-6t):

L{t^14} = 14! / s^15

L{e^(-6t)} = 1 / (s + 6)

Multiplying these two Laplace transforms together:

L{t^14 * e^(-6t)} = (14! / s^15) * (1 / (s + 6))

Simplifying the expression:

L{t^14 * e^(-6t)} = 14! / (s^15 * (s + 6))

Therefore, the Laplace transform of f(t) = t^14 * e^(-6t) is F(s) = 14! / (s^15 * (s + 6))

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What is the slope of the line

What is the slope of the line

Answers

Answer:

2/3

Step-by-step explanation:

rise over run is 2 over 3, and it is positive because the y increases as the x increases!

pls help middle school math

pls help middle school math

Answers

Given ,

5<x<10 and 8<y<19

For y-x,

8-5<y-x<19-10

3<y-x<9

PLZ PLZ PLZ PLZ HELP HELP HELP HELPFind the area of the shape.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.

PLZ PLZ PLZ PLZ HELP HELP HELP HELPFind the area of the shape.Either enter an exact answer in terms of

Answers

Answer:

3.14

Step-by-step explanation:

The formula for the area of a circle is \(\pi r^2\), where r is the radius. In this circle, the area would therefore be \(3.14\cdot 2^2=12.56\). However, since this is only a quarter circle, you need to divide the area by 4, meaning that the area of this shape is 3.14 square units. Hope this helps!

Answer:

π

Step-by-step explanation:

calculate the the full circle: A = π*\(r^{2}\) = π*\(2^{2}\) = π*4 (the area of the full circle)

you've got 1/4 or the circle according to the picture, so divide the area of the full circle with 4:

(π*4)/4 = π

Convert 5 ounces into kilograms. Round your answer to the nearest hundredth.

Answers

Answer:

Answer: 0.141 kilos

0.141748

Step-by-step explanation:

The conversion is 0.1417475 Kg

What is Unit conversion?

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects.

given:

5 ounces

So, to convert ounces to kilogram we have

1 ounce = 0.0283495 Kg

So, 5 ounces = 5* 0.0283495

5 ounces = 0.1417475 Kg

Hence, 5 ounces = 0.1417475 Kg

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