Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/6`, the angle between sides B and C is `(5pi)/12`, and the length of B is 17, what is the area of the triangle?

Answer 1

It turns out to be simply `{289}/4=72.25` square units.

Explanation:

The three angles of the triangle add up to `\pi` radians, so the angle between `A` and `C` is `\pi-(\pi/6)-({5\pi}/12)={5\pi}/12` radians.

Then the angles on both ends of side `C` are congruent and thus the triangle is isosceles, with side `A` congruent with side `B`. So side `A` measures `17` units along with side `B`. Now the area of the triangle is half the product of the two sides `A` and `B` times the sine of the angle between them:

`sin (\pi/6)=1/2`

Area = `(1/2)xx(17)xx(17)xx(1/2)={289}/4` square units.