The angles of depression of the top and the bottom of a tree as seen from the top of a tower 90 mete...........

Quantitative Aptitude ( CCS) Trignometry

The angles of depression of the top and the bottom of a tree as seen from the top of a tower 90 meters high are 30? and 60? respectively. Find the height of the tree.

40m

45m

60m

75m

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Explanation:

Let AB is the tower of height 90 m and CD is the tree.
In ΔABC, tan60⁰ =AB/AC
Height And Distances Solved
→ √3 = 90/AC
→ AC = 30√3
Hence DE = AC = 30√3m
In ΔDEB, tan30⁰ =BE/DE
→ 1/√3 = BE/30√3
→BE = 30m
Hence CD = AE = 90 – 30 = 60m.