Question

In ΔMNO, m = 9 cm, n = 8.3 cm and ∠O=35°. Find ∠N, to the nearest 10th of a degree.

Answer 1

Check the picture below.

let's firstly get the side "o", then use the Law of Sines to get ∡N.

`\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\\\\ o = √(8.3^2+9^2~-~2(8.3)(9)\cos(35^o)) \implies o = √( 149.89 - 149.4 \cos(35^o) ) \\\\\\ o \approx √( 149.89 - (122.3813) ) \implies o \approx √( 27.5087 ) \implies o \approx 5.24 \\\\[-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( N )}{8.3}\approx\cfrac{\sin( 35^o )}{5.24}\implies 5.24\sin(N)\approx8.3\sin(35^o) \implies \sin(N)\approx\cfrac{8.3\sin(35^o)}{5.24} \\\\\\ N\approx\sin^(-1)\left( ~~ \cfrac{8.3\sin( 35^o)}{5.24} ~~\right)\implies N\approx 65.30^o`

Make sure your calculator is in Degree mode.