Question

MATHEMATICS
Q. 3. The angles of elevation of the
top of a tower from two points at a
distance of 4 m and 9 m from the base of
the tower and in the same straight line
with it are complementary. Prove that the
height of the tower is 6 m.​

Answer 1

Answer:

Let angle of elevation from 4m is a. then from 9m is (90° - a).

& height of tower is h.

so,

$\tan(a) = \frac{h}{4} .....(i)$

$\tan(90 - a) = \frac{h}{9} = \cot(a) ........(ii)$

$apply \: eq \: (i) \times (ii)$

$\tan(a) \times \cot(a) = \frac{h}{4} \times \frac{h}{9}$

$\frac{ {h}^{2} }{36} = 1$

${h}^{2} = 36$

$h = 6 \: m \:$

Proved..

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