Question

Which is the area, A, of this triangle, using the formula A =1/2ab•sin(c)

Answer 1

The area of the triangle is 146.9 in²

What is the area of a triangle?

The area of a triangle given two sides and an angle or two angles can be calculated using the formula A = 1/2 ab sin (c). Here, the side (a) and (b) are the length of the sides in the given triangle and the angle c is the angle between these two sides.

Since the sides must be known, then we can say the base angles are angle A = (42°) and angle B = (50°), so the adjacent sides facing these angles can be side (a) = 21 in and side (b) = 14 in.

The determine third angle c, we have:

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

42° + 50° + ∠C = 180°

∠C = 180° - (42° + 50°)

∠C = 88°

Using the area of triangle formula:

`A =(1)/(2)* a * b * sin (c)`

`A =(1)/(2)* 21 * 14 * sin (88^0)`

A = 146.9 in²