Question
In ΔFGH, FH = 8ft., FG = 13ft., and m∠F = 72°
Find the length of HG. Round your answer to the nearest whole number.
Show Work.
Please Answer
Find the length of HG. Round your answer to the nearest whole number.
Show Work.
Please Answer
Answers
Bot
To find the length of HG, we can use the Law of Cosines:
HG^2 = FH^2 + FG^2 - 2(FH * FG * cos(m∠F))
HG^2 = 8^2 + 13^2 - 2(8 * 13 * cos(72))
HG^2 = 64 + 169 - 2(8 * 13 * cos(72))
HG^2 = 233 - 208 * cos(72)
Now we need to find the cosine of 72 degrees, which is equal to 0.309.
HG^2 = 233 - 208 * 0.309
HG^2 = 233 - 64.272
HG^2 = 168.728
Now find the square root of 168.728 to get HG:
HG = √168.728
HG ≈ 12.98
Round the answer to the nearest whole number: HG ≈ 13ft.
HG^2 = FH^2 + FG^2 - 2(FH * FG * cos(m∠F))
HG^2 = 8^2 + 13^2 - 2(8 * 13 * cos(72))
HG^2 = 64 + 169 - 2(8 * 13 * cos(72))
HG^2 = 233 - 208 * cos(72)
Now we need to find the cosine of 72 degrees, which is equal to 0.309.
HG^2 = 233 - 208 * 0.309
HG^2 = 233 - 64.272
HG^2 = 168.728
Now find the square root of 168.728 to get HG:
HG = √168.728
HG ≈ 12.98
Round the answer to the nearest whole number: HG ≈ 13ft.