Question-124953

Question Number 124953 by Algoritm last updated on 07/Dec/20

Answered by mr W last updated on 07/Dec/20

s a y A C = 1

\frac{B C}{\sin 30} = \frac{A C}{\sin 50}

\Rightarrow B C = \frac{\sin 30}{\sin 50}

s i m i l a r l y

O C = \frac{\sin 10}{\sin 20}

\frac{\sin (α + 10)}{\sin α} = \frac{B C}{O C} = \frac{\sin 30 \times \sin 20}{\sin 50 \times \sin 10}

\cos 10 + \frac{\sin 10}{\tan α} = \frac{\sin 30 \times \sin 20}{\sin 50 \times \sin 10}

\tan α = \frac{\sin 10}{\frac{\sin 30 \times \sin 20}{\sin 50 \times \sin 10} - \cos 10} = \frac{1}{\sqrt{3}}

\Rightarrow α = 30 °

Facebook Tweet Pin