Question

Express the area of the triangle shown below in terms of b and θ only.

The triangle gives the b and h, and the angle across from h (sin)

Answer 1

Given a right triangle with base, b and height, h with the angle opposide side h as θ.

The area of a triangle is given by

`A= (1)/(2) bh`

But,

`\tan\theta= (h)/(b) \\ \\ \Rightarrow h=b\tan\theta`

Therefore, the area of the triangle in terms of b and θ only is given by

`A= (1)/(2) b(b\tan\theta)= (1)/(2) b^2\tan\theta`