Question

A metal frame is constructed in the form of an isosceles trapezoid. Each base angle measures 80°, the length of the base is 7 feet, and each of the nonparallel sides is 5 feet long. Determine the length of a diagonal brace to the nearest whole number.

Answer 1

Height of a trapezoid:
h = 5 · sin 80° = 5 · 0.985 = 4.924
x = 5 · cos 80° = 5 · 0.17365 = 0.868
7 - x = 7 - 0.868 = 6.132
By the Pythagorean theorem:
d² = 6.132² + 4.924²
d² = 37.6 + 24.25
d² = 61.85
d = √61.85
d = 7.86 ≈ 8
Answer: The length of a diagonal brace is 8 feet.