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Applications of Trigonometry
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17/06/2021 11:41 am
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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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17/06/2021 11:44 am
Let AB be the building of height 7 m and EC be the height of the 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 = 7 m. and BC = AD
EC = Height of the tower
Design a figure based on given instructions:
In right ΔABC,
tan 45° = AB/BC
1= 7/BC
BC = 7
Since BC = AD
So AD = 7
Again, from right triangle ADE,
tan 60° = DE/AD
√3 = DE/7
⇒ DE = 7√3 m
Now: EC = DE + CD
= (7√3 + 7) = 7(√3+1)
Therefore, Height of the tower is 7(√3+1) m.