CBSE Class 10 Some Applications of Trigonometry Sure Shot Questions Set 07

Question. A boy is standing at some distance from a 30 m tall building and his eye level from the ground is 1.5 m. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
Answer: \( 19\sqrt{3} \text{ m} \)

Question. A ramp for unloading a moving truck, has an angle of elevation of 30°. If the top of the ramp is 0.9 m above the ground level, then find the length of the ramp.
Answer: 1.8 m.

Question. A girl standing on a light-house built on a cliff near the sea shore, observes two boats due East of the light-house. The angles of depression of the two boats are 30° and 60°. The distance between two boats is 300 m. Find the distance of the top of the light-house from the sea level. (Boats and foot of the light-house are in a straight line).
Answer: \( 150\sqrt{3} \text{ m} \)

Question. Two crows A and B are sitting at a height of 15 m and 10 m in two different trees vertically opposite to each other. They view a vadai (an eatable) on the ground at an angle of depression 45° and 60° respectively. They start at the same time and fly at the same speed along the shortest path to pick up the vadai. Which bird will succeed in it ? [Hint : Foot of two trees and vadai (an eatable) are in a straight line]
Answer: Crow B.

Question. A vertical wall and a tower are on the ground. As seen from the top of the tower, the angles of depression of the top and bottom of the wall are 45° and 60° respectively. Find the height of the wall if the height of the tower is 90 m. (Take \( \sqrt{3} = 1.732 \))
Answer: 38.04 m.

Question. A lamp-post stands at the centre of a circular park. Let P and Q be two points on the boundary such that PQ subtends an angle 90° at the foot of the lamp-post and the angle of elevation of the top of the lamp from P is 30°. If PQ = 30 m, then find the height of the lamp-post.
Answer: \( 5\sqrt{6} \text{ m} \)

Question. A person in an helicopter flying at a height of 700 m, observes two objects lying opposite to each other on either bank of a river. The angles of depression of the objects are 30° and 45°. Find the width of the river. (Take \( \sqrt{3} = 1.732 \))
Answer: 1912.40 m.

Question. A person X standing on a horizontal plane, observes a bird flying at a distance of 100 m from him at an angle of elevation of 30°. Another person Y, standing on the roof of a 20 m high building, observes the bird at the same time at an angle of elevation of 45°. If points X and Y are on the opposite sides of the bird, then find the distance of the bird from Y.
Answer: \( 30\sqrt{2} \text{ m} \)

Question. The angle of elevation of the top of a hill from the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, then find the height of the hill.
Answer: 150 m.

Question. Suppose two insects A and B can hear each other upto a range of 2 m. The insect A is on the ground and 1 m away from a wall and sees her friend B on the wall, about to be eaten by a spider. If A sounds a warning to B and if the angle of elevation of B from A is 30°, will the spider have a meal or not ? (Assume that B escapes if she hears A calling)
Answer: No.

Question. A simple pendulum of length 40 cm subtends 60° at the vertex in one full oscillation. What will be the shortest distance between the initial position and the final position of the bob ?
Answer: 40 cm.

Question. A straight highway leads to the foot of a tower. A man standing on the top of the tower spots a van at an angle of depression of 30°. The van is approaching the tower with a uniform speed. After 6 minutes, the angle of depression of the van is found to be 60°. How many more minutes will it take for the van to reach the tower ?
Answer: 3 minutes.

Question. The angles of elevation of an artificial earth satellite measured from two earth stations, situated on the same side of the satellite are found to be 30° and 60°. The two earth stations and the satellite are in the same vertical plane. If the distance between the earth stations is 4000 km, find the distance between the satellite and earth. (Use \( \sqrt{3} = 1.732 \))
Answer: 3464 km.

Question. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of 15 seconds horizontally, the angle of elevation changes to 30°. If the aeroplane is flying at a speed of 200 m/s, then find the constant height at which the aeroplane is flying.
Answer: \( 1500\sqrt{3} \text{ m} \)

Question. A student sitting in a classroom sees a picture on the black board at a height of 1.5 m from the horizontal level of sight. The angle of elevation of the picture is 30°. As the picture is not clear to him, he moves straight towards the black board and sees the picture at an angle of elevation of 45°. Find the distance moved by the student.
Answer: 1.098 m.

Question. A boy standing on the ground, spots a balloon moving with the wind in a horizontal line at a constant height. The angle of elevation of the balloon from the boy at an instant is 60°. After 2 minutes, from the same point of observation, the angle of elevation reduces to 30°. If the speed of wind is \( 29\sqrt{3} \text{ m/min} \), then find the height of the balloon from the ground level.
Answer: 87 m.

Question. The angle of elevation of a hovering helicopter as seen from a point 45 m above a lake is 30° and the angle of depression of its reflection in the lake, as seen from the same point and at the same time is 60°. Find the distance of the helicopter from the surface of the lake.
Answer: 90 m.