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Please explain how to solve image problem please explain clearly.....#......๐Ÿ™๐Ÿ™

Please explain how to solve image problem please explain clearly.....#......๐Ÿ™๐Ÿ™

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Grade:11

1 Answers

Samyak Jain
333 Points
5 years ago
Let h be the height of tower, a and b be the distances of point A (to the south wrt tower) and point B (to the east wrt tower) from the tower respectively.
Let P and Q be the top and foot of the tower. PQ = h.ย  Angles of elevation of P from A and B are \alpha and \beta.
Clearly, QAย \perp QB.ย  By Pythagoras theorem,ย  AB = d = \sqrt{a^2 + b^2}ย ย ย ย ย  โ€ฆ.(1)
In rightย \triangle PQA, \angleA = \alphaย  i.e.ย  tan\alpha = PQ/QAย  \Rightarrow tan\alpha = h/a ย \Rightarrowย  a = h cot\alpha ย ย  โ€ฆ.(2)
In right \triangle PQB, \angleB = \betaย  i.e.ย  tan\alpha = PQ/QBย  \Rightarrow tan\beta = h/bย  \Rightarrowย  b = h cot\beta ย ย  โ€ฆ.(3)
Put the values of a and b in (1). We get
dย  =ย  \sqrt{h^2cot^2\alpha + h^2cot^2\beta}ย  =ย  h \sqrt{cot^2\alpha + cot^2\beta}
\Rightarrow hย  =ย  d / \sqrt{cot^2\alpha + cot^2\beta} , which is the height of the tower.

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