# A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/6. If side B has a length of 17, what is the area of the triangle?

Apr 8, 2018

color(blue)("Area of right " Delta = (1/2) * a * b = color(maroon)(83.360 " sq units"

#### Explanation:

$b = 17 , \hat{A} = \frac{\pi}{6} , \hat{C} = \frac{\pi}{2}$

It's a right triangle with c as hypotenuse.

$\hat{B} = \pi - \frac{\pi}{6} - \frac{\pi}{2} = \frac{\pi}{3}$

Sides will be in the proportion

$a : b : c = x : \sqrt{3} x : 2 x$

$\therefore a = x = \frac{17}{\sqrt{3}} = 9.81$

color(blue)("Area of right " Delta = (1/2) * a * b = (1/2) * 9.81 * 17 = color(maroon)(83.360 " sq units"