## Heights and Distances – Aptitude General Questions & Answers!!

## Heights and Distances

Learn and practice Aptitude on “Height and Distance” with solved Aptitude Questions and Answers provided here. Check out Concepts, Formulas for Heights, and Distances. We have shared General Aptitude Question & Answers for Heights and Distances with a clear explanation.

*Angle of Elevation*

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O is called the *angle of elevation* of P as seen from O

**Angle of elevation of P from O = < AOP.**

**Angle of Depression**:

Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the *angle of depression* of P as seen from O

*Trigonometry*:

In a right-angled OAB, where BOA = ,

#### Formulas

- tan θ = sin θ / cos θ
- cot θ = cos θ / sin θ
- csc θ = 1 / sin θ
- sec θ = 1 / cos θ

### Heights and Distances Aptitude Questions & Answers

**1. On the two sides of a lighthouse, two ships sail in the sea. The angles of elevation measured from the ships on top of the lighthouse are 30 ° and 45°, respectively. Find the distance between the two ships, if the lighthouse is 100 m high.**

- A. 155.80 m
- B. 157.80 m
- C. 159. 80 m
- D. 161.80 m

**Answer:** Option B (157.80 m)

**2. A tree 24 cm tall stands near me. The tree broke and fell on a stormy night in such a way that the upper part remained fixed to the stem, forming a 30 ° angle with the ground. Find the height it broke from.**

- A. 7.5 cm
- B. 8 cm
- C. 9.5 cm
- D. 12 cm

**Answer:** Option B (8 cm)

**3. The angle of elevation, when the length of a tree’s shadow is equal to the tree’s height, is:**

- A. 45°
- B. 30°
- C. None of these
- D. 60°

**Answer:** Option A ( 45°)

**4. A man on top of a vertical observation tower observes a car moving directly toward it at a uniform speed. If the angle of depression changes from 30 ° to 45 ° in 8 minutes, how soon will the car reach the observation tower after this?**

- A. 12 min 23 second
- B. 14 min 34 second
- C. 10 min 57 second
- D. 8 min 17 second

**Answer:** Option C ( 10 min 57 seconds)

**5. A man watches a boat sailing away from the tower from the top of a hill. The Boat with the man’s eye makes an angle of depression of 45 ° when at a distance of 100 meters from the tower. Depression angle becomes 30 ° after 10 seconds. What is the Boat estimated speed, if it runs in still water?**

- A. 32.42 km/hr
- B. 26.28 km/hr
- C. 24.22 km/hr
- D. 31.25 km/hr

**Answer:** Option B ( 26.28 km/hr)

**6. A 10 m long ladder only gets to the top of a wall and makes a 60 ° angle to the roof. Find the distance from the wall to the foot of the ladder **

- A. 5 m
- B. 17.3 m
- C. 8.65 m
- D. 4.32 m

**Answer:** Option C ( 8.65 m)

**7. Raj stands in its square farm corner. The elevation angle put in the diagonally opposite corner of a scarecrow is 60 °. In a straight line, he starts walking backward, and after 80 ft, he realizes that the scarecrow elevation angle now is 30 °. What is the area of the field?**

- A. 1600, sq.ft.
- B. 40, sq.ft.
- C. 40/2 sq.ft.
- D. 800, sq.ft.

**Answer:**Option D ( 800 sq.ft.)

**8. The angle of elevation at a point X at the top of a tower is 30 °. If the elevation angle is 60 ° at point Y, on walking 30 m towards the tower, consider the tower height?**

- A. 26 m
- B. 28 m
- C. 29 m
- D. 30 m

**Answer:** Option A ( 26 m)

**9. The angles of depression at the top and bottom of a pole are 30° and 60°, respectively, from the top of a hill 100 m high. What’s the Pole Height?**

- A. 52 m
- B. 66.67 m
- C. 50 m
- D. 33.33 m

**Answer:** Option B ( 66.67 m)

**10. Two vertical poles are 200 m apart, and one’s height is twice the others. An observer finds the angular elevations of its tops complementary from the middle point of the line joining their feet. Find the heights of the poles.**

- A. 65 m and 130 m
- B. 130 m and 260 m
- C. 141 m and 282 m
- D. 70.5 m and 141 m

**Answer:** Option D ( 66.67 m)