Posted by **Anonymous** on Tuesday, February 5, 2013 at 8:33am.

a tower that is a 200 meters is leaning to one side. from a certain point on that side, the angle of elevation to the top of the tower is 70 degree. From a point 55 meters closer to the tower, the angle of elevation is 85 degree. Determine the acute angle from the horizontal at which the tower is leaning?

- trig -
**Reiny**, Tuesday, February 5, 2013 at 9:21am
First observation point A

second observation point B

top of tower P

bottom of tower Q

In triangle ABP,

angle A = 70 --- given

angle PBA = 95 --- exterior angle to 85°

angle APB = 15°

AB = 55m --- given

by the sine law

BP/sin70 = 55/sin15

BP = 55sin70/sin15

in triangle BPQ

PQ=200

angle PBQ = 85

BP = 55sin70/sin15

sinQ/BP= sin85/200

sinQ = BPsin85/200

= (55sin70/sin15)(sin85)/200 = .9946..

angle Q = 84.0658°

or appr 84°

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