Measuring the Distances of Celestial Bodies with the Help of Trigonomety

Q. If the angle of elevation of a cloud from a point 100 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake from the same point is 60°, then the height of the cloud above the lake is

1. 100 m
2. 150 m
3. 200 m
4. 250 m

Q. Calculate the shortest distance from surface of earth to moon, if the diameter(d) of earth is 12, 700km and the angle $\left(\theta \right)$ between diameter and line of sight is ${88.97}^{\circ }$ as shown in the diagram.
$tan{89}^{\circ }=57.2$

1. 3, 84, 970 km
2. 7, 54, 870 km
3. 2, 14, 475 km
4. 1, 54, 370 km

Q. An aeroplane (A) when flying at a certain height from the ground passes vertically above another aeroplane (B) at an instant when the angles of the elevation of the two aeroplanes from the same point on the ground are 30º and 45º respectively and the distance between two aeroplanes is 1000 m. Then, the approximate vertical height of the aeroplane A is $(\text{U}se\sqrt{3}=1.732)$

1. 2500 m
2. 2366 m
3. 1183 m
4. 1300 m

Q. Calculate the shortest distance from surface of earth to moon, if the diameter(d) of earth is 12, 700km and the angle $\left(\theta \right)$ between diameter and line of sight is ${88.97}^{\circ }$ as shown in the diagram.
$tan{89}^{\circ }=57.2$

1. 3, 84, 970 km
2. 7, 54, 870 km
3. 2, 14, 475 km
4. 1, 54, 370 km

Q. A circus artist is climbing on a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. If the angle made by the rope with the ground level is 60º, then the height of the pole is

1. 30 m
2. $20\sqrt{3}m$
3. 15 m
4. $30\sqrt{3}m$

Q. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. The height of the tower is .

Q.

A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?

1. 65 cm

2. 75 cm

3. 37.5 cm

4. 100 cm