Application of Trigonometry Quiz

Q1: If the length of the shadow of a tower is increasing, then the angle of elevation of the sun

Q2: The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:

Q3: If at some time, the length of the shadow of a tower is √3 times its height, then the angle of elevation of the sun, at that time is:

Q4: The shadow of a tower is equal to its height at 10-45 a.m. The sun’s altitude is

Q5: If the altitude of the sun is 60°, the height of a tower which casts a shadow of length 90m is

Q6: The angle of elevation of top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. The length of the tower is

Q7: The _ of an object is the angle formed by the line of sight with the horizontal when the object is below the horizontal level.

Q8: The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will

Q9: If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building:

Q10: A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is:

Q11: A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 60°. The height above the ground of the plane is

Q12: The top of a broken tree has its top touching the ground at a distance of 10m from the bottom. If the angle made by the broken part with the ground is 30°, then the length of the broken part is

Q13: The upper part of a tree is broken by the wind and makes an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. The height of the tree is

Q14: When the sun’s altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

Q15: If the height of a tower and the distance of the point of observation from its foot,both, are increased by 10%, then the angle of elevation of its top

Q16: If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is:

Q17: At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is:

Q18: The angles of elevation of the top of a rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is

Q19: If a kite is flying at a height of 10√3m from the level ground attached to a string inclined at 60° to the horizontal then the length of the string is

Q20: The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, the length of the wire is

Q21: A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 45o. The height of the tower will be

Q22: A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be

Q23: The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:

Q24: A person is flying a kite at a height of 30 m from the horizontal level. The length of string from the kite to the person is 60 m. Assuming that here is no slack in the string, the angle of elevation of kite to the horizontal level is:

Q25: The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 30° at a point 8m from the foot of the tree. The original height of the tree is

Q26: The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m) is:

Q27: From a point P on the level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100m high, the distance between P and the foot of the tower is

Q28: An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high.Determine the angle of elevation of the top of the tower from the eye of the observer.

Q29: The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called:

Q30: The angle of depression of a car, standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of tower (in m) is:

Q31: If the length of a shadow of a tower is increasing, then the angle of elevation of the sun is

Q32: The line drawn from the eye of an observer to the point in the object viewed by the observer is known as

Q33: The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:

Q34: The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is:

Q35: The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:

Q36: A man at the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance travelled by the car during this time interval is:

Q37: An electric pole is 10√3 m high and its shadow is 10m in length, then the angle of elevation of the sun is

Q38: If two towers of heights h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1 : h2 =

Q39: When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is

Q40: The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Then the height of tower is:

Q41: From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower standing straight is:

Q42: The angle of elevation of the top of a 15 m high tower at a point 15 m away from the base of tower is:

Q43: A man standing at a height 6 m observes the top of a tower and the foot of tower at angles of 45° and 30° of elevation and depression respectively. The height of tower is:

Q44: The angle of elevation from a point 30 feet from the base of a pole, of height h, as level ground to the top of the pole is 45°. Which equation can be used to find the height of the pole.

Q45: Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is

Q46: A contractor planned to install a slide for the children to play in a park. If he prefers to have a slide whose top is at a height of 1.5m and is inclined at an angle of 30° to the ground, then the length of the slide would be

Q47: If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is

Q48: The height or length of an object or the distance between two distant objects can be determined with the help of:

Q49: Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is:

Q50: A kite is flying at a height of 60m from the level ground, attached to a string inclined at 30° to the horizontal. The length of the string is

Q51: A portion of a 60 m long tree is broken by tornado and the top struck up the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to

Q52: A circus artist is climbing 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 30°, then the height of the pole is

Q53: If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

Q54: A 6 feet tall man finds that the angle of elevation of a 24 feet high pillar and the angle of depression of its base are complementary angles. The distance of man from the pillar is:

Q55: If altitude of the sun is 60°, the height of a tower which casts a shadow of length 30m is

Q56: The angle of elevation of top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. The length of the tower is

Q57: The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower

Q58: A lamp post 5√3 m high casts a shadow 5 m long on the ground. The sun’s elevation at this point is:

Q59: The angle of elevation from a point 30 metre from the base of tree as level ground to the top of the tree is 60°. The height of the tree is :

Q60: A circus artist is climbing a long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The ratio of the height of the pole to the length of the string is 1 :√2. The angle made by the rope with the ground level is

Q61: The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°, then the distance between the two towers is: