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- Feb 9th 2009, 02:22 PMSarahGrFinding a triangles angles from its area + 2 sides?
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- Feb 9th 2009, 02:39 PMSoroban
Hello, SarahGr!

Quote:

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: .$\displaystyle \tfrac{1}{2}ab\sin C \:=\:\text{Area}$

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

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

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

- Feb 9th 2009, 02:45 PMSarahGr
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