SSC CGL 20201)\(\)Seema flies a kite on a 16 m string at an inclination of 60 degree. What is the height of the kite above the ground?

Correct Option: D

\({8 \sqrt3} m\)

\(sin60^o = {\sqrt3 \over2}={AB \over AC}\),

\(AB = 8\sqrt3 m\)

SSC CGL 20192)From the top of a tower, the angles of depression of two objects on the ground on the same side of it, are observed to be \( 60^\circ and 30^\circ\) respectively and the distance between the objects is \(400 \sqrt3\) metre. The height (in metre) of the tower is:

Correct Option: C

600

BC = \(400 \sqrt3 \)m;

In \(\triangle ACD\),

tan \(60^0 = \frac{\sqrt{3}}{1} = \frac{AD}{CD}\);

In\( \triangle ABD\),

tan \(30^0 = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} = \frac{AD}{BD};\)

BC = BD - CD = 3 - 1 = 2 units;

2 units = 400 x

\(\sqrt{3} \)units =\( \frac{400 \sqrt3}{2} \times \sqrt{3}\) = 600 m

SSC CGL 20193)P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are \(60^0\) and \(30^0\), respectively and the distance between them is \(84\sqrt3\)m. What is the height (in m) of the pole?

Correct Option: A

63

SSC CGL 20194)From a point exactly midway between the foot of two towers P and Q,the angles of elevation of their tops are \(30^0\)and \(60^0\), respectively. The ratio of the height of P to that of Q is:

Correct Option: A

1 : 3

\(tan 30 = {1\over \sqrt{3}} = {P\over x}\) ;

\(tan 60 = { \sqrt{3}} = {Q\over x}\)

\({P\over Q} = {1\over 3}\)

SSC CGL 20165)

The angle of elevation of the top of a pillar from the foot and the top of a building 20 m high, are 60° and 30° respectively. The height of the pillar is

Correct Option: D

30 m

SSC CHSL 20216)A straight vertical pole was broken during a cyclone in such a way that its top touched the ground at a distance of \(6\sqrt 3\) m from the bottom of the pole and made and angle of 30° with the horizontal. What was the height (in m) of the pole?

Correct Option: B

18

In fig, we have to calculate P + H

tan 30° = P/6√3, P = 6m

Also, sin 30° = P/H, we get H= 12m

thus, P + H = 18m

SSC CHSL 20217)A kite is flying at a height of 138 m above the ground. It is attached to a string inclined at 45° to the horizontal. What is the approximate length (in m) of the string?

Correct Option: D

195

SSC CHSL 20218)The string of a kite is 158 m long and it makes an angle of 30° with the horizontal. What is the height (in m) of the kite ?

Assume there is no slack in the string.

Correct Option: B

79

SSC CHSL 20219)As observed from the top of a lighthouse, 42 m high above sea-level, the angle of depression of a ship sailing directly towards it changes from 30° to 45°. The distance travelled by the ship during the period of observation is:

Correct Option: A

\(42(\sqrt 3 - 1)\)

SSC CHSL 202110)The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder?

Correct Option: A

\(6\sqrt 2 \ m\)

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