Question

To find the distance from point A on the shore to point B on an island in the lake, surveyors

locate point P with m∠PAB = 65 degrees and m∠APB = 25 degrees.
By measurement, PA = 352 meters. Find AB

Answer 1

`AB=148.76\ m`

Explanation:

The complete question in the attached figure

we know that

The triangle PAB is a right triangle because the sum of ∠APB and ∠PAB is equal to 90 degrees

so

In the right triangle PAB

`sin(\angle APB)=(AB)/(AP)` ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

`sin(25^o)=(AB)/(352)`

solve for AB

`AB=sin(25^o)(352)=148.76\ m`