Finding a triangles angles from its area + 2 sides?

**SarahGr** · February 9th 2009, 02:22 PM

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**Soroban** · February 9th 2009, 02:39 PM

Hello, SarahGr!

A triangle had area of 21 cm² and two of its sides are 9 cm and 14cm long.
Find the possible measures of the angle formed by these sides?

I know the formula for the area of a triangle is ½abSin(C)
but i have no idea how to do this one.

The formula is: . $\tfrac{1}{2}ab\sin C \:=\:\text{Area}$

We are given: . $a = 9,\:b = 14,\:\text{Area} = 21$

Plug them in! . . . $\tfrac{1}{2}(9)(14)\sin C \:=\:21 \quad\Rightarrow\quad \sin C \:=\:\frac{1}{3}$

Then: . $C \;=\;\sin^{-1}\left(\tfrac{1}{3}\right) \;\approx\;19.5^o,\:160.5^o$

**SarahGr** · February 9th 2009, 02:45 PM

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