CLASS 10 · CHAPTER 09

Some Applications of Trigonometry
Practice Questions

20 curated NCERT & Board Exam questions to test your understanding. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

A 6 m high pole casts a shadow 2√3 m long on the ground. Sun's elevation is:

Q2MCQ1 Mark

If ratio of height of tower to shadow length is 1 : √3, angle of elevation of Sun is:

Q3MCQ1 Mark

Ladder leaning against wall makes angle 60° with ground. Foot is 9.5 m from wall. Length of ladder is:

Q4MCQ1 Mark

Angle of elevation of top of 100m high tower from a point 100m away from foot is:

Q5Assertion-Reason1 Mark

Assertion (A): Angle of elevation increases as the observer moves closer to the object. Reason (R): As distance from object decreases, angle subtended by object at eye increases.

Q6Assertion-Reason1 Mark

Assertion (A): Line of sight is line drawn from eye of observer to point in object viewed. Reason (R): Angle of depression is angle formed by line of sight with horizontal when object is below horizontal level.

Q7Short Answer2 Marks

A circus artist is climbing a 20 m long rope tied from top of vertical pole to ground (angle 30°). Find height of pole.

Q8Short Answer2 Marks

A tree breaks due to storm and broken top touches ground making angle 30° with ground. Distance from foot to top is 8m. Find tree height.

Q9Short Answer2 Marks

Find angle of elevation of sun when shadow of pole is √3 times its height.

Q10Short Answer2 Marks

A 1.5m tall boy looks at top of 30m tower from some distance. Angle changes from 30° to 60°. Find distance walked.

Q11Short Answer2 Marks

From point on ground, angles of elevation of bottom & top of 20m high building transmission tower are 45° & 60°. Find tower height.

Q12Long Answer3 Marks

From top of 7m high building, angle of elevation of top of cable tower is 60° and depression of foot is 45°. Find tower height.

Q13Long Answer3 Marks

As observed from top of 75m high lighthouse, angles of depression of two ships are 30° and 45°. Find distance between ships.

Q14Long Answer3 Marks

A straight highway leads to foot of tower. Man at top observes car at 30° depression. 6 seconds later depression is 60°. Find time to reach tower.

Q15Long Answer3 Marks

Angles of elevation of top of tower from two points at distances 4m and 9m from base are complementary. Prove tower height is 6m.

Q16Case Study4 Marks

Case Study Scenario: A 1.2 m tall girl spots a balloon moving horizontally at height 88.2 m. Angle changes from 60° to 30°. Question: Find distance traveled by balloon during interval.

Q17Case Study4 Marks

Case Study Scenario: A statue 1.6 m tall stands on top of pedestal. From point on ground, angle of elevation of top of statue is 60° and top of pedestal is 45°. Question: Find height of pedestal.

Q18PYQ5 Marks

An aeroplane at altitude 300m observes two ships on opposite sides of river at angles 45° and 60°. Find width of river.

Q19PYQ5 Marks

Angle of elevation of cloud from point 60m above lake is 30° and angle of depression of reflection is 60°. Find cloud height.

Q20PYQ5 Marks

Some Applications of Trigonometry Practice Questions