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

Respuesta :

Answer:

[tex]AB=148.76\ m[/tex]

Step-by-step 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

[tex]sin(\angle APB)=\frac{AB}{AP}[/tex] ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

[tex]sin(25^o)=\frac{AB}{352}[/tex]

solve for AB

[tex]AB=sin(25^o)(352)=148.76\ m[/tex]

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