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If a flag staff of 6 m high placed on the top of a tower throws a \( \Large 2\sqrt{3} m\) along the ground, then the angle (in degrees) that the sun makes with the ground is:

A) \( \Large 60 ^{\circ} \)
B) \( \Large 80 ^{\circ} \)
C) \( \Large 75 ^{\circ} \)
D) none of these

Correct Answer:

A) \( \Large 60 ^{\circ} \)

Description for Correct answer:

Triangle DCB, \( \Large \tan \theta = \frac{h}{x} \)

and in \( \Large \triangle ECA \tan \theta = \frac{h+6}{2\sqrt{3}+x} \)

=> \( \Large \frac{h}{x} = \frac{h+6}{2\sqrt{3}+x} \) [from (i)]

=> \( \Large 2\sqrt{3}h + hx = hx + 6x \)

=> \( \Large 2\sqrt{3}h = 6x => h = \frac{6x}{2\sqrt{3}} \)

From equation (i)

\( \Large \tan \theta = \frac{6x}{2\sqrt{3x}} = \sqrt{3} => \theta = 60 ^{\circ} \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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Similar Questions

1). The angle of elevation of the top of a tower from a point A due south of it, is \( \Large \tan^{-1}6 \) and that from B due west of it, is \( \Large \tan^{-1}7.5 \). If h is the height of the tower, then AB = xh, where \( \Large x^{2} \) is equal to:

A). \( \Large \frac{21}{700} \)

B). \( \Large \frac{42}{1300} \)

C). \( \Large \frac{41}{900} \)

D). none of these

2). An observer standing on a 300 m high tower obeserver see two boat in the same direction, their angles of depression are \( \Large 60 ^{\circ} \) and \( \Large 30 ^{\circ} \) respectively. The distance between boats is:

A). 173.2 m

B). 346.4 m

C). 25 m

D). 72 In

3). A pole stands vertically inside a triangular par ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then is park the foot of the pole is at the:

A). centroid

B). circumcentre

C). incentre

D). ortho centre

4). The angle of elevation of the top of the tower observed from each of the three points A, B, C on the ground forming a triangle is the same angle \( \Large \alpha \). If R is the circumradius of the triangle ABC, then the height of the tower is

A). \( \Large R \sin \alpha \)

B). \( \Large R \cos \alpha \)

C). \( \Large R \cot \alpha \)

D). \( \Large R \tan \alpha \)

5). From of 60 m high tower angles of depression of the top and bottom of a house are \( \Large \alpha \) and \( \Large \beta \) respectively. If the height of the house is \( \Large \frac{60 \sin \left( \beta - \alpha \right) }{x} \) is equal, then x:

A). \( \Large \sin \alpha \sin \beta \)

B). \( \Large \cos \alpha \cos \beta \)

C). \( \Large \sin \alpha \cos \beta \)

D). \( \Large \cos \alpha \sin \beta \)

6). An aeroplane flying horizontally 1 km above the ground is observed at an elevation of \( \Large 60 ^{\circ} \) and after 10sec. the elevation is observed to be \( \Large 30 ^{\circ} \). The uniform speed of the aeroplane (in km/h) is:

A). 240

B). \( \Large 240\sqrt{3} \)

C). \( \Large 60\sqrt{3} \)

D). none of these

7). A spherical balloon of radius r subtends an anagle \( \Large \alpha \) at the eye of an observer. If the angle of elevation of the centre of the balloon be \( \Large \beta \), the height of the centre of the balloons is:

A). \( \Large r cosec \left(\frac{ \alpha }{2}\right) \sin \beta \)

B). \( \Large r cosec \alpha \sin \left(\frac{ \beta }{2}\right) \)

C). \( \Large r \sin \left(\frac{ \alpha }{2}\right) cosec \beta \)

D). \( \Large r \sin \alpha cosec \left(\frac{ \beta }{2}\right) \)

8). ABC is a triangular park with AB = AC = 100 m. A clock tower is situated at the mid point of BC. The angles of elevation of the top of the tower at A and B are \( \Large \cot^{-1}3.2 \) and \( \Large cosec^{-1}2.6 \) respectively. The height of the tower is:

A). 50 m

B). 25 m

C). 40 m

D). none of these

9). The upper \( \Large \frac{3}{4} \)th portion of a vertical pole subtends an angle \( \Large \tan^{ -1}\frac{3}{5} \) at a point in the horizontal plane through its foot and a distance 40 m from the foot. A possible height of the vertical pole is

A). 20 m

B). 40 m

C). 60 m

D). 80 m

10). Three vertical towers standing at A, B, C subtends the angle \( \Large \theta _{A} \), \( \Large \theta _{B} \) and \( \Large \theta _{C} \) respectively at the circum centre of the triangle ABC then \( \Large \tan \theta _{A} \), \( \Large \tan \theta _{B} \) and \( \Large \tan \theta _{C} \) are in

A). AP

B). GP

C). HP

D). none of these