# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is (pi)/2 and the angle between B and C is  (pi)/3. What is the area of the triangle?

Feb 12, 2016

≈ 15.6

#### Explanation:

since the angle between A and C is $\frac{\pi}{2}$
then triangle ABC is right , with hypotenuse B.

the area is therefore $\frac{1}{2} A C$

To find C , use Pythagoras' Theorem.

$C = \sqrt{{8}^{2} - {5}^{2}} = \sqrt{64 - 25} = \sqrt{39}$

hence area =  1/2 xx 5 xx sqrt39 ≈ 15.6