the angle of depression of the top and the foot of a flagpole as seen from the top of a building145 metres away are 26 degree and 34 degree respectively .find the heights of pole and the building?

5 answers

Make your sketch.
I labelled the top of the building P and its bottom Q, the top of the pole A and its bottom B.
So QA = 145 m
Enter all the given angles, after that all angles at A and B can be found
In triangle PQB , angle PBQ = 34° and
tan 34 = PQ/145
PQ = ..... <----- the height of the building

Using cos 34 = 145/PB , you can find PB

In triangle ABP, you know all the angles, and the side PB
Use the sine law to find AB
h1 = ht. of flagpole.
h2 = distance from top of flagpole to top of bldg.
(h1+h2) = ht. of bldg.

Tan34 = (h1+h2)/145.
(h1+h2) =145*Tan34 = 98 m. = ht. of bldg.

Tan26 = h2/145.
h2 = 145*Tan26 = 71 m.

h1 = (h1+h2) - h2 = 98 - 71 = 27 m. = ht. of flagpole.
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