Question-177205

Question Number 177205 by HeferH last updated on 02/Oct/22

Answered by mr W last updated on 02/Oct/22

∠ C A D = 180 - 120 - 3 x = 60 - 3 x

∠ C D B = 180 - 3 x

a p p l y i n g l a w o f s i n e s :

\frac{\sin (60 - 3 x)}{C D} = \frac{\sin 120}{A D} \dots (i)

\frac{C D}{\sin 2 x} = \frac{C B}{\sin (180 - 3 x)} \dots (i i)

A D = C B

(i) \times (i i) :

\frac{\sin (60 - 3 x)}{\sin 2 x} = \frac{\sin 120}{\sin (180 - 3 x)}

\frac{\sin (60 - 3 x)}{\sin 2 x} = \frac{\sqrt{3}}{2 \sin 3 x}

\Rightarrow x \approx 8.02 °

Commented by Tawa11 last updated on 02/Oct/22

Great sir

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