Question

Given: ∆PST, PT = 8, m∠T = 90°, m∠S = 48° Find: perimeter of ∆PTS

Answer 1

`P=25.97\ units`

Explanation:

see the attached figure to better understand the problem

we know that

The perimeter of triangle PST is equal to

`P=PT+PS+TS`

step 1

Find the length PS

In the right triangle PST

`sin(48\°)=(PT)/(PS)` ---> opposite side angle of 48 degrees divide by the hypotenuse

substitute the given values

`sin(48\°)=(8)/(PS)`

Solve for PS

`PS=(8)/(sin(48\°))`

`PS=10.765\ units`

step 2

Find the length TS

In the right triangle PST

`cos(48\°)=(TS)/(PS)` ---> adjacent side angle of 48 degrees divided by the hypotenuse

substitute the given values

`cos(48\°)=(TS)/(10.77)`

Solve for TS

`TS=cos(48\°)(10.765)`

`TS=7.203\ units`

step 3

Find the perimeter

`P=PT+PS+TS`

we have

`PT=8\ units`

`PS=10.765\ units`

`TS=7.203\ units`

substitute

`P=8+10.765+7.203=25.968\ units`