Question

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

Answer 1

Answer:

$P=25.98\ units$

Step-by-step 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

$sin(48\°)=\frac{PT}{PS}$ ---> opposite side angle of 48 degrees divide by the hypotenuse

substitute the given values

$sin(48\°)=\frac{8}{PS}$

Solve for PS

$PS=\frac{8}{sin(48\°)}$

$PS=10.77\ units$

step 2

Find the length TS

In the right triangle PST

$cos(48\°)=\frac{TS}{PS}$ ---> adjacent side angle of 48 degrees divide by the hypotenuse

substitute the given values

$cos(48\°)=\frac{TS}{10.77}$

Solve for TS

$TS=cos(48\°)(10.77)$

$TS=7.21\ units$

step 3

Find the perimeter

$P=PT+PS+TS$

we have

$PT=8\ units$

$PS=10.77\ units$

$TS=7.21\ units$

substitute

$P=8+10.77+7.21=25.98\ units$