Question

In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=54°, and OP = 68 feet. Find the length of PQ to the nearest foot.

Answer 1

`PQ=40\ ft`

Explanation:

see the attached figure to better understand the problem

we know that

In the right triangle OPQ

`cos(P)=(PQ)/(OP)` ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

`cos(54^o)=(PQ)/(68)`

solve for PQ

`PQ=(68)cos(54^o)=40\ ft`