Question

plz solve this question

Answer 1

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Since you have the 42-deg angle and the length of the opposite side, 31, you can use the Law of Sines.


\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}sinAa​=sinBb​=sinCc​


We will use the law of sines first to find x.

Once we know x, we can find the angle opposite y.

Then we can find y.


\dfrac{31}{\sin 42^\circ} = \dfrac{37}{\sin x}sin42∘31​=sinx37​


\sin x = \dfrac{37\sin 42^\circ}{31}sinx=3137sin42∘​


\sin x = 0.798639sinx=0.798639


x = \sin^{-1} 0.798639 = 53^\circx=sin−10.798639=53∘


Let z = the angle opposite y.


z + 42 + 53 = 180


z = 85

\dfrac{31}{\sin 42^\circ} = \dfrac{y}{\sin 85^\circ}sin42∘31​=sin85∘y​


y = \dfrac{31 \sin 85^\circ}{\sin 42^\circ}y=sin42∘31sin85∘​


y = 46.2y=46.2