Question

In triangle ABC, a = 3, b = 7, and angle C = 86º. Find the area of the triangle correct to the nearest tenth?

Answer 1

`a=3`
`b=7`
`C=86°`

Explanation:

The area of a triangle is: `T=(h*b)/2`
If we draw a line from the top angle `B` perpendicular to `b`, we get a right triangle. The angle `C` is opposite to `h`:
`sin(C)=h/a => h=sin(C)*a`
`T=(h*b)/2= (sin(C)*a*b)/2= (sin(86°)*3*7)/2=11.5`

There are other methods to calculate the area of a triangle, sometime Heron's formula can be useful.