In ∆FGH, FH = 8ft, FG = 13 ft,
and m< F = 72. Find the length of HG. Label the diagram to help you. Round your answer to the nearest whole number.
Hg=?
Answer 13 ft
To solve the problem, we can use the law of cosines which states that c^2 = a^2 + b^2 - 2ab*cos(C), where c is the length of the side opposite the angle C, and a and b are the lengths of the other two sides.
In this case, we can label HG as side c, FG as side a, and FH as side b. Then, angle F is opposite side a.
Substituting the given values, we have:
HG^2 = 13^2 + 8^2 - 2(13)(8)*cos(72)
HG^2 = 169 + 64 - 208*cos(72)
HG^2 ≈ 169 + 64 - 60.06 (using a calculator to find cosine of 72 degrees)
HG^2 ≈ 172.94
Taking the square root of both sides, we get:
HG ≈ 13 ft (rounded to the nearest whole number)
Therefore, the length of HG is approximately 13 ft.