Question

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?

Answer 1

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

Explanation:

`b = 17, hat A = pi/6, hat C = pi/2`

It's a right triangle with c as hypotenuse.

`hat B = pi - pi/6 - pi/ 2 = pi/3`

Sides will be in the proportion

`a : b : c = x : sqrt3 x : 2 x`

`:. a = x = 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"`