Question

please answer these questions​

Answer 1

Answer:

Given, the angles of elevation of the top of tower from the two points are complementary. Thus, the height of the tower is 6 m.

Answer 2

Answer:

${ \huge{ \pmb{ \sf{★Required \: Answer... }}}}$

Let the height of the tower = h m

AC be a horizontal line on a ground.

A and B are the two points on a line at a distance 9m and 4m from the base of tower.

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${ \sf{Let \: \angle{CBD} = \theta \: and \: \angle{CAD} = 90 - \theta}}$

( complementary mean sum of two angles is equal to 90°)

In right angle ΔACD,

${ \sf{tan(90 - \theta) = \frac{CD}{AC} \implies{cot \theta = \frac{h}{9}...(1) } }}$

In right angle ΔBCD,

${ \sf{tan \theta = \frac{CD}{BC} \implies{tan \theta = \frac{h}{4}...(2) } }}$

From equation (1) &(2), We get,

$: { \implies { \sf{tan \theta \times cos \theta = \frac{h}{9} \times \frac{h}{4} }}}$

$\: : { \implies { \sf{1 = \frac{ {h}^{2} }{36} }}}$

$\: : { \implies { \sf{ {h}^{2} = 36}}}$

$\: : { \implies { \sf{h = \sqrt{36} }}}$

$\: : { \implies { \sf{h = 6m}}}$

Therefore,

• Height of the tower = 6m

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