Answer the following questions, using trigonometry rules.
Class 10th CBSE, Rd Sharma, some applications of trigonometry
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13. On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.
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Solution:
Given,
The height of the tower (AB) = 150m
Angles of depressions of the two objects are 45o and 60o.
In ΔABD
tan 45o = AB/ BD
1 = 150/ BD
BD = 150m
Next, in ΔABC
tan 60o = AB/ BC
√3 = 150/ BC
BC = 150/√3
BC = 50√3 = 50(1.732) = 86.6 m
So,
DC = BD – BC = 150 – 86.6 = = 63.4
Therefore, the distance between two objects = 63.4 m