1)

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:

SSC CGL 2019

A)

800

B)

\(800\sqrt3\)

C)

600

D)

\(600\sqrt3\)

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

2)

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?

SSC CGL 2019

A)

63

B)

73.5

C)

52.5

D)

60

3)

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:

SSC CGL 2019

A)

1 : 3

B)

1 : 2

C)

\(1:2\sqrt3\)

D)

\(2 : 3\sqrt3\)

Correct Option: A

1 : 3

---

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

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

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