Answer:
11.1 feet
Explanation:
When you are given a right triangle with a given angle and side, you can use
trigonometric functions to calculate missing side lengths or inverse functions for angles based on this information.
These ratios can be remembered by the mnemonic:
SOH CAH TOA.
S O H → Sin (Sine) = Opposite / Hypotenuse
C A H → Cos (Cosine) = Adjacent / Hypotenuse
T O A → Tan (Tangent) = Opposite / Adjacent
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The Opposite side is the side directly across from the angle, The adjacent (next to) side is the side other than the hypotenuse or opposite side, and the hypotenuse is the longest side.
Given that we are trying to find the adjacent side, we must use the cos (cosine) function because that can be multiplied by the hypotenuse to give us the adjacent side we are looking for.
Therefore, 36 [Hypotenuse Side] × cos(72°) = Adjacent Side.
Because: 36 = Hypotenuse Side.
cos(72)° = Adjacent Side / Hypotenuse Side.
36 × cos(72°) =
36 × 0.309016994374... = 11.12461179749... ≈ 11.1