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A vertical pole on a 15° slope is braced by a wire from the top of the pole
to a point 20 ft. uphill from the base. If the pole subtends an angle of 62°30'
from this point, find the height of the pole and length of the wire.
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Let point A be the base of the pole;
point B be the upper end of the pole,
and point C be the point where the wire is attached to the slope of the hill.
We have triangle ABC with this given information:
- angle C is 62°30';
- angle A is 90° - 15° = 75°;
- side AC is 20 ft long.
They want you find side c = AB (the pole height) and the side a = BC (the length of the wire).
First, we find the measure of the angle B: it is 180° - 62°30' - 75° = 42°30'.
Next, write sine law proportion
= = .
To find side c = AB, use this part of the proportion
= , = , = ,
which gives c = = 26.26 ft (the height of the pole). ANSWER
To find side a = BC, use this part of the proportion
= , = , = ,
which gives a = = 28.59 ft (the length of the wire). ANSWER
Solved.