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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)

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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
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