Question

In ΔHIJ, i = 5.5 inches, j = 3.9 inches and ∠H=78°. Find ∠I, to the nearest 10th of an degree.

Answer 1

we'll do the same as you saw on the earlier one, we'll find side "h" and then use the Law of Sines to get ∡I.

`\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\\\\ h = √(5.5^2+3.9^2~-~2(5.5)(3.9)\cos(78^o)) \implies h = √( 45.46 - 920.205 \cos(78^o) ) \\\\\\ h \approx √( 45.46 - (8.9194) ) \implies h \approx √( 36.5406 ) \implies h \approx 6.04`

now let's get the Law of Sines

`\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(78^o)}{6.04}=\cfrac{\sin(I)}{5.5}\implies \sin^(-1)\left[ \cfrac{5.5\sin(78^o)}{6.04} \right]\approx \measuredangle I\implies 63.0^o\approx \measuredangle I`