Question

What is the area of a triangle with A=15°, B=113°, and b=7?

Answer 1

C

Explanation:

First, use the sine rule:

`(b)/(\sin B)=(a)/(\sin A),\\ \\(7)/(\sin 113^(\circ))=(a)/(\sin 15^(\circ)),\\ \\a=(7\sin 15^(\circ))/(\sin 113^(\circ))\approx 1.968\ un.`

Now, the sum of the measures of all interior angles of the triangle is equal to 180°,

`\angle C=180^(\circ)-113^(\circ)-15^(\circ)=52^(\circ).`

At last, the area of the triangle is

`A=(1)/(2)ab\sin \angle C,\\ \\A=(1)/(2)\cdot 1.968\cdot 7\cdot \sin 52^(\circ)\approx 5.4\ un^2.`