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.
In ΔFGH, FH = 8ft, FG = 13ft, and m∠F = 72°
Find the length of HG. Round your answer to the nearest whole number
you should get 13
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