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 5, what is the area of the triangle?

Answer 1

since one of the angles is 90 degrees, we have a right triangle with 90 / 30 and 60 degree angles.

tan 30 = opp/adj
tan 30 = A/B sides given

so A = 5tan30 or approximately 2.89

the area of a triangle is A = 1/2 base x height
we already know the base and height of this right triangle as they are the two legs of the right triangle (A and B)
using base of 5 and height of 2.89, we obtain the area as:

A = 1/2 x (5)(2.89) or approx. 7.22 square units