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CBSE
Class 10
Mathematics
Mathematics
Some Applications of Trigonometry

Question Bank

Practice Hub

Question Bank: Some Applications of Trigonometry

Structured practice
Question Practice

Practice chapter questions in a cleaner, exam-ready flow

Start with curated question sets, move into full module views when needed, and keep discovering related practice without losing your place in the chapter.

Question Bank - Some Applications of Trigonometry

View all (74)
Q1.

What is the angle of elevation when a person looks at the top of a tree from a point 30 m away at an angle of 45°?

Single Answer MCQ
Q-00174123
View explanation
Q2.

If the height of a building is 24 m and the angle of elevation from a point on the ground 10 m away from its base is 60°, what would be the height of the observer's eyes if the height of the building is added?

Single Answer MCQ
Q-00174124
View explanation
Q3.

A person standing on the ground observes a balloon at an angle of elevation of 30°. If the balloon rises to a height where the angle of elevation is now 60°, how will this affect the height calculated?

Single Answer MCQ
Q-00174125
View explanation
Q4.

From a point 50 m away from the base of a tower, the angle of elevation to the top of the tower is 45°. What is the height of the tower?

Single Answer MCQ
Q-00174126
View explanation
Q5.

If a student is 1.5 m tall and stands 20 m away from a tree, forming an angle of elevation of 60°, how tall is the tree?

Single Answer MCQ
Q-00174127
View explanation
Q6.

When a girl looks down at a flower pot from an angle of depression of 30° from a height of 10 m, what is the horizontal distance to the pot?

Single Answer MCQ
Q-00174128
View explanation
Q7.

What happens to the perceived height of an object when the observer moves further away?

Single Answer MCQ
Q-00174129
View explanation
Q8.

If a collector views an object from 45 m away at an angle of elevation of 30°, how do you calculate the height of the object?

Single Answer MCQ
Q-00174130
View explanation
Q9.

A hill is observed from the ground at a distance of 100 m with an angle of elevation of 45°. What is the vertical height of the hill?

Single Answer MCQ
Q-00174131
View explanation
Q10.

Which of the following best describes the angle of depression?

Single Answer MCQ
Q-00174132
View explanation
Q11.

For a man 1.75 m tall looking up at a lamppost with an angle of elevation of 60° standing 25 m away, how can you find the height of the lamppost?

Single Answer MCQ
Q-00174133
View explanation
Q12.

What effect does increasing the distance from the object have on the angle of elevation if the height remains unchanged?

Single Answer MCQ
Q-00174134
View explanation
Q13.

If a tower is 40 m high and an observer sees it from 30 m away with an angle of elevation of 60°, what is the relationship between the height of the tower and the observed height?

Single Answer MCQ
Q-00174135
View explanation
Q14.

A kite flying at an angle of elevation of 45° from a point 20 m away from the base of a tree makes which geometry in sighting?

Single Answer MCQ
Q-00174136
View explanation
Q15.

From a point 10 m away from the base of a tower, the angle of elevation to the top of the tower is 60°. What is the height of the tower?

Single Answer MCQ
Q-00174137
View explanation
Q16.

An observer 1.2 m tall is standing 25 m away from a building. If the angle of elevation to the top of the building from the observer's eyes is 30°, what is the height of the building?

Single Answer MCQ
Q-00174138
View explanation
Q17.

A tree casts a shadow of 15 m when the angle of elevation of the sun is 45°. What is the height of the tree?

Single Answer MCQ
Q-00174139
View explanation
Q18.

Find the height of a flagpole if a person standing 20 m away observes it with an angle of elevation of 60°.

Single Answer MCQ
Q-00174140
View explanation
Q19.

A lighthouse is 50 m tall. If a boat is 100 m away from the base of the lighthouse, what is the angle of elevation to the top of the lighthouse?

Single Answer MCQ
Q-00174141
View explanation
Q20.

An observer is standing at the ground level and looks at the top of a tree with an angle of elevation of 30°. If the tree is 10 m tall, how far is the observer from the base of the tree?

Single Answer MCQ
Q-00174142
View explanation
Q21.

A flagstaff on a hill has a height of 12 m. From a point on the same level as the base of the hill, the angle of elevation to its top is 45°. What is the distance from this point to the base of the hill?

Single Answer MCQ
Q-00174143
View explanation
Q22.

A tower stands vertically on the ground. If a person is standing 10 m away from the base of the tower and the angle of elevation to the top of the tower is 30°, what is the height of the tower?

Single Answer MCQ
Q-00174144
View explanation
Q23.

The angle of elevation of the sun when the length of the shadow of a 20 m tall tree is 10 m is what?

Single Answer MCQ
Q-00174145
View explanation
Q24.

From a point 50 m away from a building, the angle of elevation to the top of the building is 60°. What is the height of the building?

Single Answer MCQ
Q-00174146
View explanation
Q25.

If the angle of elevation from the foot of a hill to a tower is 60° and the height of the tower is 30 m, find the distance to the foot of the hill.

Single Answer MCQ
Q-00174147
View explanation
Q26.

An observer 1.8 m tall is standing 30 m away from a tree. If the angle of elevation to the top of the tree is 45°, what is the height of the tree?

Single Answer MCQ
Q-00174148
View explanation
Q27.

A person standing 50 m away from a monument sees it at an angle of elevation of 55°. Find the height of the monument.

Single Answer MCQ
Q-00174149
View explanation
Q28.

If a ladder makes an angle of elevation of 60° with the ground and reaches a point 4 m up on the wall, how long is the ladder?

Single Answer MCQ
Q-00174150
View explanation
Q29.

What is the height of a tower whose angle of elevation at a point 30 m away is 45°?

Single Answer MCQ
Q-00174151
View explanation
Q30.

The height of a building is 12 m. From the top of the building, the angle of depression to a point on the ground is 30°. What is the distance of the point from the base of the building?

Single Answer MCQ
Q-00174152
View explanation
Q31.

A tree is observed at an angle of elevation of 30°. If the distance to the tree from the observer is 25 m, what height can be expected?

Single Answer MCQ
Q-00174153
View explanation
Q32.

A flagstaff of height x meters is erected on a building of height 15 m. From a point 30 m away from the building, the angle of elevation to the top of the flagstaff is 60°. What is the value of x?

Single Answer MCQ
Q-00174154
View explanation
Q33.

If the angle of elevation changes from 30° to 60°, how does the height of a building remain constant but change the observed distance?

Single Answer MCQ
Q-00174155
View explanation
Q34.

The shadow of a pole is found to be 10 m long when the angle of elevation of the sun is 60°. How tall is the pole?

Single Answer MCQ
Q-00174156
View explanation
Q35.

A man 1.8 m tall observes a building from a distance of 10 m, noticing it's 2 m taller than him. What is the angle of elevation from where he stands?

Single Answer MCQ
Q-00174157
View explanation
Q36.

An observer is standing 20 m away from a vertical pole. If the angle of elevation from the observer's eyes (at a height of 1.5 m) to the top of the pole is 30°, what is the height of the pole?

Single Answer MCQ
Q-00174158
View explanation
Q37.

The angles of elevation from the ground to the top and bottom of a 10 m tall building are 30° and 10°, respectively. Find the distance of the observer from the base of the building.

Single Answer MCQ
Q-00174159
View explanation
Q38.

From a point 45 m away from a building, the angle of elevation to the top of the building is 60° and the angle of depression to the bottom is 30°. How tall is the building?

Single Answer MCQ
Q-00174160
View explanation
Q39.

From the top of a multi-storeyed building, the angles of depression of two points on the ground are 30° and 45°. If the height of the building is H, what is the distance between the two points on the ground?

Single Answer MCQ
Q-00174161
View explanation
Q40.

An observer's height is 1.75 m. If they stand 15 m from a tree and observe it at an angle of elevation of 45°, what is the height of the tree?

Single Answer MCQ
Q-00174162
View explanation
Q41.

A tower stands vertically on the ground. From a point on the ground, which is 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 30°. What is the height of the tower?

Single Answer MCQ
Q-00174163
View explanation
Q42.

What is the angle of depression?

Single Answer MCQ
Q-00174164
View explanation
Q43.

An observer 1.2 m tall is standing 15 m away from a lamp post. The angle of elevation of the top of the lamp post from her eyes is 60°. What is the height of the lamp post?

Single Answer MCQ
Q-00174165
View explanation
Q44.

A person is standing on a hill and looking down at a point on the ground that is 30 m below. If the angle of depression is 45°, what is the horizontal distance from the person to the point?

Single Answer MCQ
Q-00174166
View explanation
Q45.

From a point on the ground, the angle of elevation of a quayside crane is 45° and it is 10 m away. What is the height of the crane?

Single Answer MCQ
Q-00174167
View explanation
Q46.

From a tower, the angle of depression to the foot of a hill is 30°. If the height of the tower is 20 m, how far is the foot of the hill from the base of the tower?

Single Answer MCQ
Q-00174168
View explanation
Q47.

The shadow of a building is 50 m long when the angle of elevation of the sun is 30°. Find the height of the building.

Single Answer MCQ
Q-00174169
View explanation
Q48.

If the angle of depression from a point A on a building is 60° to a point B on the ground, and the distance from A to B vertically is 10 m, what is the horizontal distance from the base of the building to point B?

Single Answer MCQ
Q-00174170
View explanation
Q49.

From the top of a 50 m high tower, the angle of depression to a point on the ground is 30°. How far away is the point from the base of the tower?

Single Answer MCQ
Q-00174171
View explanation
Q50.

When observing a ship at sea, if the angle of depression from the top of a lighthouse is 30° and the lighthouse is 50 m high, how far is the ship from the base of the lighthouse?

Single Answer MCQ
Q-00174172
View explanation
Q51.

Two towers are 100 m apart. The angles of elevation to the top of each tower from the foot of the other tower are 45° and 30°, respectively. Compute the heights of the towers.

Single Answer MCQ
Q-00174173
View explanation
Q52.

If a person looks down at an angle of depression of 40° to the foot of a tree and the tree is 10 m tall, what is the distance of the person from the base of the tree?

Single Answer MCQ
Q-00174174
View explanation
Q53.

When the angle of elevation of the sun is 60°, the shadow of a tree is 5 m long. What is the height of the tree?

Single Answer MCQ
Q-00174175
View explanation
Q54.

From the top of a hill, the angle of depression to a point on the ground is measured to be 55°. If the distance from the hill to the point is 200 m, what is the height of the hill?

Single Answer MCQ
Q-00174176
View explanation
Q55.

An observer standing 10 m away from a vertical cliff measures the angle of elevation to the top of the cliff to be 45°. Determine the height of the cliff.

Single Answer MCQ
Q-00174177
View explanation
Q56.

A lookout tower has a height of 80 m. If the angle of depression to a ship is 30°, how far is the ship from the base of the tower?

Single Answer MCQ
Q-00174178
View explanation
Q57.

A building casts a shadow of 60 m when the angle of elevation of the sun is at 30°. Find the height of the building.

Single Answer MCQ
Q-00174179
View explanation
Q58.

If the angle of elevation to the top of a building is 70° and the angle of depression to the base of the building is 40°, find the height of the building if the observer is 20 m away.

Single Answer MCQ
Q-00174180
View explanation
Q59.

From a point on a bridge 5 m above the ground, the angles of depression to two points of the banks of a river are 30° and 60°. Calculate the width of the river.

Single Answer MCQ
Q-00174181
View explanation
Q60.

A drone is flying at a height of 50 m. If the angle of depression to a car on the ground is 25°, how far is the car from the point directly below the drone?

Single Answer MCQ
Q-00174182
View explanation
Q61.

A ladder leans against a wall forming an angle of elevation of 60° with the ground. If the ladder is 10 m long, how high does the ladder reach on the wall?

Single Answer MCQ
Q-00174183
View explanation
Q62.

An observer sees a tower with an angle of elevation of 30° standing on a 10 m hill. If the observer is 40 m away from the foot of the hill, what is the height of the tower?

Single Answer MCQ
Q-00174184
View explanation
Q63.

What is the angle of elevation from a point 10 m away from a tree that is 8 m tall?

Single Answer MCQ
Q-00174200
View explanation
Q64.

If the angle of depression from the top of a tower is 30°, what is the relationship between the height of the tower and the horizontal distance to the observer at its foot?

Single Answer MCQ
Q-00174201
View explanation
Q65.

From a point on the ground, the angle of elevation to the top of a building is 45°. If the observer is 20 meters away from the building, what is the height of the building?

Single Answer MCQ
Q-00174202
View explanation
Q66.

If the angle of elevation to the top of a hill is 60° and the distance from the observer to the base is 30 m, what is the height of the hill?

Single Answer MCQ
Q-00174203
View explanation
Q67.

A ladder 10 m long leans against a wall, forming an angle of 60° with the ground. How high up the wall does the ladder reach?

Single Answer MCQ
Q-00174204
View explanation
Q68.

What is the angle of depression if the height of an object is 15 m and the distance from the observer to the base of the object is 20 m?

Single Answer MCQ
Q-00174205
View explanation
Q69.

If a person is standing 40 m away from a building and the angle of elevation to the top is 30°, what is the height of the building?

Single Answer MCQ
Q-00174206
View explanation
Q70.

In a right triangle, if the height is 24 m and the base is 10 m, what is the angle of elevation from the base to the top?

Single Answer MCQ
Q-00174207
View explanation
Q71.

What will be the angle of elevation if a person measures the height of a pole to be 25 m standing 30 m away from its base?

Single Answer MCQ
Q-00174208
View explanation
Q72.

A drone is flying at an angle of 45° above the ground and is 20 m away horizontally from the observer. How high is the drone?

Single Answer MCQ
Q-00174209
View explanation
Q73.

If the angle of depression to the bottom of a well from a point 25 m above the ground is 53°, what is the depth of the well?

Single Answer MCQ
Q-00174210
View explanation
Q74.

A person standing on the ground sees the top of a building at an angle of elevation of 30°. If the building is 10 m tall, how far is the person from the base?

Single Answer MCQ
Q-00174211
View explanation
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