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
$A= \frac{1}{2} bh$

But,
$\tan\theta= \frac{h}{b} \\ \\ \Rightarrow h=b\tan\theta$

Therefore, the area of the triangle in terms of b and θ only is given by
$A= \frac{1}{2} b(b\tan\theta)= \frac{1}{2} b^2\tan\theta$