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As shown in the diagram, a pole TF is on the roof of a shed FB. From a point P on the ground 27 feet from the foot of the shed, the measure of the angle to the of the pole T is 38º. The measure of the angle to the foot of the pole F is 32º. Determine to the nearest tenth of a foot, the height of the pole. (Hint: To find length TF, first determine length TB in right triangle TBP. Then determine FB in right triangle FBP. Subtract length FB from length TB to determine TF.)

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taskmasters

I visualize it as a right triangle. I'll use the tangent function.

Angle is given: 32° and 38°
adjacent is given: 27 feet.
we need to look for the value of opposite.

tan θ = opposite / adjacent
opposite = tan θ   adjacent
opposite = tan 32° 27 feet 
opposite = 16.87 feet

opposite = tan 38° * 27 feet 
opposite = 21.09 feet

21.09 feet - 16.87 feet = 4.22 feet

The height of the pole is 4.22 feet.

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