Here we are with 48 Height & Distance Aptitude Questions that are slightly challenging. The questions are divided into 3 parts, each with 16 questions. All the questions are real exam-style problems and unique. Every question trains students in the angles of elevation and depression in a practical way. You will learn how to spot the right triangle quickly. You will also know when to use tan, sin, and cos without confusion. Try them only after you fully understand the basics and your fundamentals are clear with the trigonometry formulas.
We have more aptitude question and answers.
Height & Distance: Core Formulas
Symbols (meaning shown once)
- θ: angle (in degrees unless stated)
- h: vertical height (m, cm, etc.)
- d: horizontal distance from observer to the foot/base (m, km, etc.)
- D₁, D₂: two different horizontal distances (same unit as d)
- α, β: two different angles (often from two observation points)
- AB: perpendicular (vertical side)
- OA: base (horizontal side)
- OB: hypotenuse (slant side)
Right-Triangle Trigonometry
- sin θ = AB ÷ OB
- cos θ = OA ÷ OB
- tan θ = AB ÷ OA
- cosec θ = 1 ÷ sin θ = OB ÷ AB
- sec θ = 1 ÷ cos θ = OB ÷ OA
- cot θ = 1 ÷ tan θ = OA ÷ AB
Trig Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
Standard Values (0°, 30°, 45°, 60°, 90°)
- sin θ: 0, 1/2, 1/√2, √3/2, 1
- cos θ: 1, √3/2, 1/√2, 1/2, 0
- tan θ: 0, 1/√3, 1, √3, not defined
Angle Terms
- Angle of Elevation: angle between line of sight and the horizontal when looking up
- Angle of Depression: angle between line of sight and the horizontal when looking down
Height–Distance Relations (using tan)
- tan θ = h ÷ d
- h = d × tan θ
- d = h ÷ tan θ
Two-Point Observation (common derived formulas)
- If the same object is observed from two points on the same straight line with angles α (nearer) and β (farther), and the distance between the two points is x:
- h = x × (tan α × tan β) ÷ (tan α − tan β)
- If the horizontal distances from the object are known as D₁ and D₂:
- h = D₁ × tan α = D₂ × tan β
Shadow / Ladder Style Relations
- If s is shadow length (or horizontal base of ladder):
- tan θ = h ÷ s
- h = s × tan θ
- If L is ladder length (hypotenuse) and it makes angle θ with the ground:
- sin θ = h ÷ L
- cos θ = s ÷ L
- h = L × sin θ
- s = L × cos θ
48 Height & Distance Aptitude Questions and Answers (Solved MCQs)
Question 1. From a point on level ground, the angle of elevation of a tower is 30°. If the point is 80 m from the tower, find the height of the tower.
a) 40√3 m
b) 80/√3 m
c) 80√3 m
d) 40/√3 m
Answer:
b) 80/√3 m – h = 80 x tan(30°)
Question 2. A tree casts a shadow of 20 m when the sun’s elevation is 45°. Find the height of the tree.
a) 10 m
b) 20 m
c) 20√2 m
d) 40 m
Answer:
b) 20 m — tan45° = 1.
Question 3. A tower and its shadow measure 36 m and 12√3 m respectively. Find the sun’s elevation.
a) 30°
b) 45°
c) 60°
d) 75°
Answer:
c) 60° — tanθ = 36/(12√3) = √3.
Question 4. The angle of elevation of the top of a building from a point is 60°. If the building is 45 m high, find the distance of the point from the building.
a) 15√3 m
b) 15 m
c) 45√3 m
d) 30 m
Answer:
a) 15√3 m — distance = 45/√3.
Question 5. From a point, the angle of elevation of a pole is 45°. If the point is 24 m from the pole, find the pole’s height.
a) 12 m
b) 24 m
c) 24√2 m
d) 48 m
Answer:
b) 24 m
Question 6. A ladder 26 m long reaches the top of a wall. If the ladder makes 60° with the ground, find the wall’s height.
a) 13 m
b) 13√3 m
c) 26/√3 m
d) 26√3 m
Answer:
b) 13√3 m — height = 26 × sin60°.
Question 7. A kite is at a height of 60 m. The string makes 30° with the ground. Find the length of the string (straight).
a) 60 m
b) 120 m
c) 60√3 m
d) 30√3 m
Answer:
b) 120 m — sin30° = 1/2.
Question 8. A man 1.8 m tall sees the top of a tree at 45° from his eye level. If he stands 18 m from the tree, find the tree’s height.
a) 18 m
b) 19.8 m
c) 20.8 m
d) 21.6 m
Answer:
b) 19.8 m — Extra height = 18×tan45°.
Question 9. From a point, angle of elevation of a tower is 30°. From a point 40 m closer, the angle becomes 60°. Find the tower’s height.
a) 20√3 m
b) 40√3 m
c) 60√3 m
d) 80/√3 m
Answer:
a) 20√3 m
Question 10. A flagpole is observed at 60° from a point. If the height is 15√3 m, find the distance from the point.
a) 5 m
b) 10 m
c) 15 m
d) 20 m
Answer:
c) 15 m
Question 11. A tower’s angle of elevation is 30°. If its height is 50 m, find the distance of the observation point.
a) 25√3 m
b) 50√3 m
c) 100√3 m
d) 150 m
Answer:
b) 50√3 m
Question 12. A boy stands 30 m from a tower. The angle of elevation is 60°. Find the height of the tower.
a) 10√3 m
b) 15√3 m
c) 30√3 m
d) 60√3 m
Answer:
c) 30√3 m
Question 13. A building casts a 15 m shadow when the sun’s elevation is 30°. Find the building’s height.
a) 5√3 m
b) 10√3 m
c) 15√3 m
d) 30/√3 m
Answer:
a) 5√3 m
Question 14. A tower and a point on ground form an angle of elevation 45°. If the tower is 28 m high, find the distance to the point.
a) 14 m
b) 28 m
c) 28√2 m
d) 56 m
Answer:
b) 28 m
Question 15. A ramp of length 20 m rises to a platform. If it makes 30° with the ground, find the platform height.
a) 5 m
b) 10 m
c) 10√3 m
d) 20 m
Answer:
b) 10 m — height = 20×sin30°.
Question 16. The angle of depression from a cliff top to a boat is 30°. If the cliff is 60 m high, find the boat’s horizontal distance from the cliff base.
a) 20√3 m
b) 30√3 m
c) 60√3 m
d) 120/√3 m
Answer:
c) 60√3 m — tan30° = 60/d.
Question 1. From a point A, angle of elevation of a tower is 30°. From point B, 60 m nearer to the tower, the angle is 60°. Find the tower’s height.
a) 20√3 m
b) 30√3 m
c) 40√3 m
d) 60√3 m
Answer:
b) 30√3 m
Question 2. From A, elevation is 45°. After moving 20 m towards the tower to B, elevation becomes 60°. Find the height.
a) 10√3 m
b) 27.3 m
c) 30√3 m
d) 40√3 m
Answer:
b) 27.3 m
Question 3. From A, a building top is seen at 30°. From B, 50 m farther from the building, the elevation is 15°. Find the building’s height.
a) 25 m
b) 25√3 m
c) 50/√3 m
d) 50 m
Answer:
a) 25 m — h = x/√3 = (x+50)tan15°.
Question 4. From A, a tower’s elevation is 60°. From B, 30 m farther away (same line), elevation is 45°. Find the tower’s height.
a) 30 m
b) 30√3 m
c) 71 m
d) 60 m
Answer:
c) 71 m
Question 5. From two points A and B on level ground, 100 m apart, elevations of a tower are 30° and 60° respectively. Find the tower’s height.
a) 25√3 m
b) 50√3 m
c) 75 m
d) 100/√3 m
Answer:
b) 50√3 m — Use h = x/√3 and h = √3(100−x).
Question 6. From A, elevation is 45°. From B, which is 40 m farther, elevation is 30°. Find the height.
a) 20 m
b) 54.9 m
c) 20√3 m
d) 40√3 m
Answer:
b) 54.9 m
Question 7. From A, angle of elevation of a tower is 60°. The observer moves away 30 m to B; angle becomes 30°. Find the tower’s height.
a) 10√3 m
b) 15√3 m
c) 20√3 m
d) 30√3 m
Answer:
b) 15√3 m
Question 8. From A, elevation is 30°. From B, 80 m closer, elevation is 45°. Find the tower’s height.
a) 109 m
b) 80/√3 m
c) 80 m
d) 40√3 m
Answer:
a) 109 m
Question 9. From A, elevation to top is 45°. From B, 60 m closer, elevation becomes 75°. Find the tower’s height.
a) 30 m
b) 60 m
c) 30(2+√3) m
d) 60(2+√3) m
Answer:
c) 30(2+√3) m — tan75° = 2+√3.
Question 10. A man observes a tower at 30°. He walks 40 m towards it and sees 60°. Find the initial distance from the tower.
a) 20 m
b) 40 m
c) 60 m
d) 80 m
Answer:
c) 60 m — Let d; d/√3 = √3(d−40).
Question 11. From A, elevation of a building is 45°. From B, 25 m farther, elevation is 30°. Find the building’s height.
a) 25 m
b) 25√3 m
c) 34.15 m
d) 75/√3 m
Answer:
c) 34.15 m
Question 12. Two points A and B are 60 m apart in a straight line with a tower between them. Elevations are 30° from A and 45° from B. Find the tower’s height.
a) 21.9 m
b) 20√3 m
c) 30 m
d) 30√3 m
Answer:
a) 21.9 m
Question 13. From A, elevation is 60°. From B, 20 m farther, elevation is 45°. Find the distance from A to tower.
a) 10 m
b) 27.3 m
c) 30 m
d) 40 m
Answer:
b) 27.3 m
Question 14. From A, elevation is 15°. From B, 100 m closer, elevation is 45°. Find the height.
a) 50 m
b) 75 m
c) 100 tan15° m
d) 100 m
Answer:
a) 50 m — h = x tan15 = (x−100).
Question 15. A tower is observed from A at 30°. After moving 90 m towards it to B, elevation becomes 60°. Find the tower’s height.
a) 30√3 m
b) 45√3 m
c) 60√3 m
d) 90/√3 m
Answer:
b) 45√3 m
Question 16. From A, elevation is 45°. From B, 30 m closer, elevation is 60°. Find the tower’s height.
a) 15√3 m
b) 30√3 m
c) 71 m
d) 60 m
Answer:
c) 71 m
Question 1. From the top of a 50 m building, the angle of depression of a car is 30°. Find the car’s distance from the building base.
a) 25√3 m
b) 50√3 m
c) 100/√3 m
d) 75 m
Answer:
b) 50√3 m — tan30° = 50/d.
Question 2. From the top of a 60 m cliff, angles of depression of two boats in the same line are 30° and 45°. Find the distance between the boats.
a) 60(√3−1) m
b) 60(√3+1) m
c) 60(1−1/√3) m
d) 60(√3) m
Answer:
a) 60(√3−1) m — d = 60cot.
Question 3. Two towers of heights 60 m and 40 m stand 100 m apart. Find the angle of elevation of the taller tower from the top of the shorter tower.
a) tan⁻¹(1/5)
b) tan⁻¹(1/2)
c) tan⁻¹(1/3)
d) tan⁻¹(2/5)
Answer:
a) tan⁻¹(1/5) — Vertical diff 20 over 100.
Question 4. From a point on ground, angles of elevation of the top and bottom of a billboard on a building are 60° and 45°. If the bottom is 20 m above ground, find the billboard’s height.
a) 20(√3−1) m
b) 20(√3+1) m
c) 20(1−1/√3) m
d) 20√3 m
Answer:
a) 20(√3−1) m — Same distance, subtract heights.
Question 5. A 30 m tower stands on a 20 m building. From a point on ground, angle of elevation to top is 60°. Find distance from point to building base.
a) 25 m
b) 50/√3 m
c) 50√3 m
d) 40 m
Answer:
b) 50/√3 m — Total height 50, tan60.
Question 6. A river is crossed by observing a tree on the opposite bank. From point A, elevation to top is 30°. From point B, 40 m nearer, elevation is 45°. Find the tree’s height.
a) 20 m
b) 20(1 + √3) m
c) 40 m
d) 40√3 m
Answer:
b) 20(1 + √3) m
Question 7. From the top of a 45 m building, the angle of depression to point P is 60°. From P, the angle of elevation to the top of the building is:
a) 30°
b) 45°
c) 60°
d) 75°
Answer:
c) 60° — Depression equals elevation (alternate angles).
Question 8. A tower is broken at a point and the top touches the ground 18 m from its base. If the remaining vertical part is 24 m, find the original height.
a) 30 m
b) 36 m
c) 42 m
d) 54 m
Answer:
d) 54 m
Question 9. A 20 m pole stands on a 10 m hill. From a point on level ground, angle of elevation to pole top is 45°. Find the distance from point to hill foot.
a) 20 m
b) 30 m
c) 10√3 m
d) 40 m
Answer:
b) 30 m — Total height 30; tan45.
Question 10. Two points A and B are on opposite sides of a tower in the same straight line. Angles of elevation are 30° and 60°. If AB = 90 m, find tower’s height.
a) 15√3 m
b) 22.5√3 m
c) 30√3 m
d) 45√3 m
Answer:
b) 22.5√3 m
Question 11. DATA SUFFICIENCY: Find the height of a tower.
I. From a point 60 m away, the elevation is 30°.
II. From a point 40 m away, the elevation is 45°.
a) I alone sufficient
b) II alone sufficient
c) Both together sufficient, neither alone
d) Either I or II alone
Answer:
d) Either I or II alone
Question 12. DATA SUFFICIENCY: Find the distance of a point from a building.
I. Building height is 45 m and elevation is 60°.
II. Building height is 45 m and elevation is 45°.
a) I alone sufficient
b) II alone sufficient
c) Both together sufficient, neither alone
d) Both statements independently
Answer:
d) Both statements independently
Question 13. A tower and a building are 40 m apart. From the top of the 30 m building, the angle of elevation of the tower top is 45°. Find the tower’s height.
a) 50 m
b) 60 m
c) 70 m
d) 80 m
Answer:
b) 70? Wait: extra height = 40tan45 = 40; tower=30+40=70.
Question 14. A statue stands on a 20 m pedestal. From a point, angles of elevation to statue top and pedestal top are 60° and 45°. If statue height is h, find h.
a) 20(√3−1) m
b) 20(√3+1) m
c) 20/√3 m
d) 20√3 m
Answer:
a) 20(√3−1) m
Question 15. From the top of a 36 m building, angle of depression of a point P is 45°. From P, angle of elevation of a 12 m pole on the building top is:
a) 30°
b) 45°
c) 60°
d) tan⁻¹(4/3)
Answer:
d) tan⁻¹(4/3) — Distance = 36; total height 48.
Question 16. A man observes the top of a tower at 30°. After climbing a 10 m platform at same spot, the elevation becomes 45°. Find the tower’s height.
a) 10(1+√3) m
b) 10(2+√3) m
c) 5(3+√3) m
d) 20√3 m
Answer:
c) 5(3+√3) m
