Question

In ΔRST, r = 18 inches, s = 46 inches and ∠T=158°. Find ∠R, to the nearest degree.

Answer 1

Check the picture below.

let's firstly find side "t"

`\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = √(a^2+b^2-(2ab)\cos(C)) \\\\[-0.35em] ~\dotfill\\\\ t = √(18^2+46^2~-~2(18)(46)\cos(158^o)) \implies t = √( 2440 - 1371168 \cos(158^o) ) \\\\\\ t \approx √( 2440 - (-1535.42) ) \implies t \approx √( 3975.42 ) \implies t \approx 63.05 \\\\[-0.35em] ~\dotfill`

`\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin( R )}{18}\approx\cfrac{\sin( 158^o )}{63.05}\implies 63.05\sin(R)\approx18\sin(158^o) \\\\\\ \sin(R)\approx\cfrac{18\sin(158^o)}{63.05} \implies R\approx\sin^(-1)\left( ~~ \cfrac{18\sin( 158^o)}{63.05} ~~\right)\implies \boxed{R\approx 6.14^o}`

Make sure your calculator is in Degree mode.