estimates the angle of elevation to the same tower to be 48degrees.

Question

A suspension bridge has two main towers of equal height. A visitor on a tour ship approaching the bridge estimates that the angle of elevation to one of the towers is 13 degrees. After sailing 408 ft closer he estimates the angle of elevation to the same tower to be 48degrees. Approximate the height of the tower.

Answer 1

Draw the schematic diagram

From the triangle ABC.

tan(48) =h/d

d= h/tan(48)                                    ...... (1)

From the triangle ABD.

tan(13) =h/(d+408)                              ...... (2)

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From the equations (1) and (2).

tan(13) =h/((h/tan(48))+408)

0.231=h/(0.9h+408)

h=0.231(0.9h+408)

h=0.2079h+94.25

0.7921h=94.25

h= 119 ft