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Question

Question 12
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 45. Determine the height of the tower.

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Solution

Let AB be the building of height 7 m and EC be the height of tower.
A is the point from where elevation of tower is 60 and the angle of depression of its foot is 45.

EC=DE+CD
Also, CD=AB=7m and BC=AD
According to question,
In right ΔABC,
tan 45=ABBC
1=7BC
BC=7m=AD
Also,
In right ΔADE,
tan 60=DEAD
3=DE7
DE=73m
Height of the tower =EC=DE+CD =(73+7)m=7(3+1)m

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