In ΔFGH, FH = 8ft, FG = 13ft, and m∠F = 72°

Question

Find the length of HG. Round your answer to the nearest whole number

you should get 13

Show Work.
Please Answer.

Answer 1

To find the length of HG, we will use the Law of Cosines. The Law of Cosines states:

c² = a² + b² - 2ab*cos(C)

where a, b, and c are the side lengths of a triangle, and C is the angle opposite side c. In this problem, we have:

- FH = a = 8 ft
- FG = b = 13 ft
- m∠F = C = 72°

We want to find the length of HG, which we will call c. Plugging these values into the Law of Cosines formula, we get:

c² = 8² + 13² - 2(8)(13)*cos(72°)

Now, we compute the value of each term:

c² = 64 + 169 - 2(8)(13)*cos(72°)

Next, we find the cosine of 72 degrees:

cos(72°) ≈ 0.309

Now we plug this value back into the equation:

c² = 64 + 169 - 2(8)(13)*0.309
c² = 64 + 169 - 166.912
c² ≈ 66.088

Now, we find the square root of this value to get the length of HG:

c ≈ √66.088
c ≈ 8.13

Rounding to the nearest whole number, we get:

c ≈ 8

So, the length of HG is approximately 8 feet.