Question

17. The area of a triangle is 1718.58 square meters. We know two of itssides are 67 meters and 113 meters. Use the area formula for Triangles shown below to determine the measure of the included angle betweenthese two sides.A = 1/2a•b• sin C

Answer 1

The given formula is

`A=(1)/(2)a\cdot b\cdot\sin C`

Then, we replace all the given magnitudes

`1718.58m^2=(1)/(2)\cdot67m\cdot113m\cdot\sin C`

Now, we solve for angle C.

`\begin{gathered} 2\cdot1718.58m^2=7571m^2\cdot\sin C \\ (3437.16m^2)/(7571m^2)=\sin C \\ C=\sin ^(-1)((3437.16)/(7571)) \\ C\approx27 \end{gathered}`

Hence, angle C measures 27°.