From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The angle of elevation of the top of a water tank (on the top of the tower) is 45°. Find

(i) the height of the tower,


(ii) the depth of the tank.

In the figure assume, A to be the point 40m away from the foot of the tower BC. Join A,B and A,C and A,D. Let DC be the water tank and BC be the tower. We get two right-angled triangles ABC and ABD, right angled at B. Also, ∠ BAC = 30° and ∠ BAD = 45°. We use trigonometric ratios tan using AB as base and BC as height(for ∆ABC) and AB as base and CD as height(for ∆ABD). Let BC be x.


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In ∆ABC,



or,



So, BC = 23.09m.


In ∆ABD,



or,



i. Height of the tower = BC = 23.1m


ii. Depth of the tank = DC = 16.9m


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