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State if the following is true or false.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are $α$ and $β$ respectively, then the height of the tower is $h tan α tan β − tan α$ .

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True

False

answer is A.

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Detailed Solution

We need to find whether the height of the tower is

.
Let the height of the tower be

B C = x

A B = h C D = y

and

∠ C D B = α

and

∠ C B A

β

Now,

So, height of the tower is

h t a n α tan β − t a n α

.
Therefore, the statement is true.
Hence, option 1 is correct.

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