From the top of a tower 75m high the angles of depression of the top and bottom of a pole standing o...........

Quantitative Aptitude ( CCS) Height and Distance

From the top of a tower 75m high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be 30⁰ and 45⁰ respectively. Find the height of the pole.

30.4m

35.9m

28.6m

31.7m

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Explanation:

Let AB is the tower of height 75 m and CD is the pole, such that ∠BDE = 30⁰ and ∠BCA = 45⁰
In ΔBAC, tan 45⁰ = AB/AC
Height & Distances
⇒ 1 = AB/AC ⇒ AB = AC ⇒ AC = 75m
Now DE = AC = 75m
In ΔBED,
tan 30⁰ = BE/DE
⇒ 1/√3 = BE/75 ⇒ BE = 75/√3m
⇒ BE = 25√3m = 43.3 m
Hence the height of the pole
= CD = AE = AB – BE = 75 – 43.3 = 31.7m