Question

A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is `(3pi)/8` and the angle between B and C is `(5pi)/24`. What is the area of the triangle?

Answer 1

area ≈ 9.66 square units

Explanation:

The area of the triangle can be found using `1/2ABsintheta`
where `theta " is the angle between A and B."`

since the sum of the 3 angles in a triangle is `pi`

Then the angle `theta = pi -((3pi)/8 + (5pi)/24)`

`rArr theta = pi - (7pi)/12 = (5pi)/12`

`rArr "area " = 1/2 xx 4 xx 5 xx sin((5pi)/12) ≈ 9.66`