Find alpha angle

Geometry Level pending


The answer is 18.

Aly Ahmed by Aly Ahmed , 34, Egypt

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1 solution

sin ⁡ 54 = A B 2 \sin 54=\dfrac{AB}{2}

A B = 2 sin ⁡ 54 AB = 2 \sin 54

Y B = A B − 1 = 2 sin ⁡ 54 − 1 YB = AB - 1 = 2 \sin 54 - 1

sin ⁡ α = Y B 2 = 2 sin ⁡ 54 − 1 2 \sin \alpha=\dfrac{YB}{2}=\dfrac{2 \sin 54 - 1}{2}

α = sin ⁡ − 1 2 sin ⁡ 54 − 1 2 = 1 8 ∘ \alpha=\sin^{-1}\dfrac{2 \sin 54 - 1}{2}=\boxed{18^\circ}

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