Question

The area of triangle ABC is 3√2 square inches. Find the measure of the acute angle, A, if b = 9 meters and c = 2 meters.

14°
28°
42°
71°

Answer 1

The answer is 28 degrees. 

Answer 2

The measure of angle C is 28°

Explanation:

Given the area of triangle ABC is 3√2 square inches.

we have to find the measure of angle A if b=9 m and c=2 m

As area of triangle can be calculated as

`Area=(1)/(2)* b* c* \Sin C`

`3\sqrt2=(1)/(2)* 9* 2* \sin C`

`\sin C=(3\sqrt2 * 2)/(9* 2)=(\sqrt2)/(3)`

`C=sin^(-1)((\sqrt2)/(3))=28.125\sim 28^(\circ)`

Option 2 is correct.