Question

Find the area of the triangle, is side a=12.7, side b=8.6 and the angle between them(C) is
73 degrees. Hint: Find the area using the formula
Area=(1/2)*a*b*sin(C).

Answer 1

Task. Find the area of the triangle, is side $a=12.7$, side $b=8.6$ and the angle between them $\gamma$ is 73 degrees.

Solution. It is known that the area of the triagne wit two sides $a$ and $b$ and the angle $\gamma$ between them can be computed by the following formula:

$S=\frac{1}{2}ab\sin\gamma.$

In our case

$a=12.7,\qquad b=8.6,\qquad\gamma=73{}^{\circ}.$

Then

$\sin\gamma=\sin 73{}^{\circ}\approx 0.95630,$

and substituting the values to the above formula we get

$S=\frac{1}{2}ab\sin\gamma=\frac{1}{2}*12.7*8.6*0.95630\approx 52.2.$

Answer. $S=52.2.$