Question

I need help!!!ONLY write your answer as a number. You do not needto write the unit measurement.Round you answer to the nearest tenth.Find PS.

Answer 1

To find the values of side PS we can use the trignometric functions to find the different measures of the 2 right triangles on the image.

First start by finding the measure of side QS using the triangle on the right ant the angle of 28°.

The trigonometric function taht involves the side given QR and the missing side QS is the tan.

`\begin{gathered} \tan (28)=(QS)/(QR) \\ QS=QR\cdot\tan 28 \\ QS=39\cdot\tan (28) \end{gathered}`

after having the value of QS express side PS using the sin of 76°

`\begin{gathered} \sin 76=(QS)/(PS) \\ PS=(QS)/(\sin 76) \\ PS=(39\cdot\tan (28))/(\sin (76)) \\ PS\approx21.4 \end{gathered}`