Question
In ΔFGH, FH = 8ft, FG = 13ft, and m∠F = 72°
Find the length of HG.
you should get 13
Show Work.
Please Answer.
Find the length of HG.
you should get 13
Show Work.
Please Answer.
Answers
Bot
We can use the Law of Cosines to solve for the length of HG:
c² = a² + b² - 2ab cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
In this case, we want to solve for HG (which is the side opposite angle F), so we can label a = FH = 8ft, b = FG = 13ft, and C = m∠F = 72°.
c² = 8² + 13² - 2(8)(13) cos(72°)
c² = 64 + 169 - 208cos(72°)
c² ≈ 169
c ≈ 13
Therefore, the length of HG is approximately 13ft, as we expected.
c² = a² + b² - 2ab cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
In this case, we want to solve for HG (which is the side opposite angle F), so we can label a = FH = 8ft, b = FG = 13ft, and C = m∠F = 72°.
c² = 8² + 13² - 2(8)(13) cos(72°)
c² = 64 + 169 - 208cos(72°)
c² ≈ 169
c ≈ 13
Therefore, the length of HG is approximately 13ft, as we expected.