from a point a metre above a lake the angle of elevation of

From a point a metre above a lake the angle of elevation of a cloud is $$\alpha $$ and the angle of depression of its reflection is $$\beta .$$ The height of the cloud is

A. $$\frac{{a\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\alpha - \beta } \right)}}{\text{metre}}$$

B. $$\frac{{a\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\beta - \alpha } \right)}}{\text{metre}}$$

C. $$\frac{{a\sin \left( {\alpha - \beta } \right)}}{{\sin \left( {\alpha + \beta } \right)}}{\text{metre}}$$

D. None of these

Answer : $$\frac{{a\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\beta - \alpha } \right)}}{\text{metre}}$$

Solution :
$$\left( {H + a} \right)\cot b = \left( {H - a} \right)\cot a$$
using componendo and dividendo
$$ \Rightarrow H = \frac{{a\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\beta - \alpha } \right)}}$$
Properties and Solutons of Triangle mcq solution image

Properties and Solutons of Triangle mcq solution image

Releted MCQ Question on
Trigonometry >> Properties and Solutons of Triangle

Releted Question 1

If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S,$$ then

A. $$QS = SR$$

B. $$QS : SR = PR : PQ$$

C. $$QS : SR = PQ : PR$$

D. None of these

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Releted Question 2

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is

A. $$\left( {\frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}} \right)60\,{\text{metres}}$$

B. $$\left( {\frac{{\sqrt 3 + 1}}{{\sqrt 3 - 1}}} \right)60\,{\text{metres}}$$

C. $${\left( {\frac{{\sqrt 3 + 1}}{{\sqrt 3 - 1}}} \right)^2}{\text{metres}}$$

D. none of these

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Releted Question 3

In a triangle $$ABC,$$ angle $$A$$ is greater than angle $$B.$$ If the measures of angles $$A$$ and $$B$$ satisfy the equation $$3\sin x - 4{\sin ^3}x - k = 0, 0 < k < 1,$$ then the measure of angle $$C$$ is

A. $$\frac{\pi }{3}$$

B. $$\frac{\pi }{2}$$

C. $$\frac{2\pi }{3}$$

D. $$\frac{5\pi }{6}$$

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Releted Question 4

In a triangle $$ABC,$$ $$\angle B = \frac{\pi }{3}{\text{ and }}\angle C = \frac{\pi }{4}.$$ Let $$D$$ divide $$BC$$ internally in the ratio 1 : 3 then $$\frac{{\sin \angle BAD}}{{\sin \angle CAD}}$$ is equal to

A. $$\frac{1}{{\sqrt 6 }}$$

B. $${\frac{1}{3}}$$

C. $$\frac{1}{{\sqrt 3 }}$$

D. $$\sqrt {\frac{2}{3}} $$

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From a point a metre above a lake the angle of elevation of a cloud is $$\alpha $$ and the angle of depression of its reflection is $$\beta .$$ The height of the cloud is

Releted MCQ Question on
Trigonometry >> Properties and Solutons of Triangle

If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S,$$ then

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is

In a triangle $$ABC,$$ angle $$A$$ is greater than angle $$B.$$ If the measures of angles $$A$$ and $$B$$ satisfy the equation $$3\sin x - 4{\sin ^3}x - k = 0, 0 < k < 1,$$ then the measure of angle $$C$$ is

In a triangle $$ABC,$$ $$\angle B = \frac{\pi }{3}{\text{ and }}\angle C = \frac{\pi }{4}.$$ Let $$D$$ divide $$BC$$ internally in the ratio 1 : 3 then $$\frac{{\sin \angle BAD}}{{\sin \angle CAD}}$$ is equal to

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Properties and Solutons of Triangle

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From a point a metre above a lake the angle of elevation of a cloud is $$\alpha $$ and the angle of depression of its reflection is $$\beta .$$ The height of the cloud is

Releted MCQ Question on Trigonometry >> Properties and Solutons of Triangle

If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S,$$ then

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is

In a triangle $$ABC,$$ angle $$A$$ is greater than angle $$B.$$ If the measures of angles $$A$$ and $$B$$ satisfy the equation $$3\sin x - 4{\sin ^3}x - k = 0, 0 < k < 1,$$ then the measure of angle $$C$$ is

In a triangle $$ABC,$$ $$\angle B = \frac{\pi }{3}{\text{ and }}\angle C = \frac{\pi }{4}.$$ Let $$D$$ divide $$BC$$ internally in the ratio 1 : 3 then $$\frac{{\sin \angle BAD}}{{\sin \angle CAD}}$$ is equal to

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Trigonometry >> Properties and Solutons of Triangle

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Properties and Solutons of Triangle