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