ICSE Class 10 Answered
A pillar stands on top of cliff. from a point on the ground 40m away from the base, the angles of elevation of the top of the pillar and the top of the cliff are 60° and 45° respectively. Find the height of the pillar.
please send the full answer with workings
Asked by shethdhanesh | 20 Oct, 2023, 17:59: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/37f2f4d4c76028e73b68feb9cb13bbca6532c7ef9bc0b8.37991013f1.png)
Figure shows a pillar of height AB above a cliff of height BC.
From a point D which is at distance 40 m from the cliff , angle of elevation of bottom of a pillar is 45°.
Hence we get
![begin mathsize 14px style fraction numerator B C over denominator C D end fraction space equals space tan 45 degree space equals space 1 end style](https://images.topperlearning.com/topper/tinymce/cache/8ac7ae3836529476274f649411dc2f9c.png)
Hence BC = CD = 40 m .
From a point D, angle of elevation of top of a pillar is 60°.
![begin mathsize 14px style fraction numerator A C over denominator D C end fraction equals tan 60 space equals space square root of 3 end style](https://images.topperlearning.com/topper/tinymce/cache/37adb1adec27a2363a87da140a5d782c.png)
Hence we get AC = 40√3 m
Pillar height AB = AC - BC = 40 ( √3 - 1 ) m = 29.3 m
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