Question

Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest hundredth (two decimal places).

Answer 1

In the right angle triangle PQS,

`\begin{gathered} sin62.58^(\circ)=(PS)/(PQ) \\ \sin 62.58^(\circ)=(PS)/(4.5) \\ PS=4.5\sin 62.58^(\circ) \\ PS=3.99 \end{gathered}`

Thus, value of PS is 3.99 units.

The value of QS can be determined as,

`\begin{gathered} \cos 62.58=(QS)/(PQ) \\ QS=4.5\cos 62.58 \\ QS=2.07 \end{gathered}`

Thus, the value of QS is 2.07 units.

The area of triangle PQR can be determined as,

`\begin{gathered} \Delta=(1)/(2)* QR* PS \\ =(1)/(2)*(5+2.07)*3.99 \\ =14.10 \end{gathered}`

Thus, the required area is 14.10 square units.