Answer :
The length of h to the nearest inch is 78 inches.
What is Law of Cosines?
Law of cosines of triangle states that for three length of sides of the triangle, a, b and c opposite to the angles A, B and C respectively can be related as,
a² = b² + c² - 2bc cos(A)
Given that, In ΔFGH,
f = 83 inches, g = 11 inches and ∠H = 60°.
Using the law of cosines,
h² = f² + g² - 2fg cos(H)
Substituting,
h² = 83² + 11² - (2 × 83 × 11) cos (60°)
= 7010 - (1826 × 1/2)
= 7010 - 913
= 6097
h = √6097 = 78.083 inches ≈ 78 inches
Hence the length of h is 78 inches.
Learn more about Law of Cosines here :
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