All questions of Height & Distance for SSC CGL Exam

Understanding the Problem
The problem involves a man observing a tower from two different distances, with angles of elevation of 30° and 60°. We need to find the distance between the base of the tower and the initial point P.
Key Points to Consider
- Angles of Elevation:
- At Point P: 30°
- After walking towards the tower: 60°
- Trigonometric Relationships:
- The tangent of an angle in a right triangle refers to the opposite side divided by the adjacent side.
Setting Up the Equations
1. Initial Position (Point P):
- Let the height of the tower be h and the distance from P to the base of the tower be d.
- Using the angle of elevation (30°):
- tan(30°) = h/d
- h = d * (1/√3)
2. After Walking Towards the Tower:
- Let the distance walked towards the tower be x.
- The new distance from the base of the tower is (d - x).
- Using the angle of elevation (60°):
- tan(60°) = h/(d - x)
- h = (d - x) * √3
Solving the Equations
- Set the two expressions for h equal:
- d * (1/√3) = (d - x) * √3
- Solve for x in terms of d:
- d/√3 = d√3 - x√3
- Rearranging gives:
- x = d(√3 - 1/√3)
Conclusion
To find the exact distance d, we would need additional information about either the height of the tower or the distance the man walked towards it. Hence, the answer is:
Correct Answer: Data inadequate
Thus, without further information, we cannot determine the exact distance between the base of the tower and point P.

Understanding the Problem
To calculate the height of the tower, we need to visualize the scenario involving the building and the tower. The building is 10 m high, and we have two angles of elevation:
- Angle of elevation to the top of the tower: 60°
- Angle of depression to the foot of the tower: 45°
Visual Representation
Imagine the following:
- A vertical line representing the building’s height (10 m).
- A line extending from the top of the building to the top of the tower at a 60° angle.
- A line extending from the top of the building down to the foot of the tower at a 45° angle.
Applying Trigonometry
1. Finding the horizontal distance to the tower (d):
- From the top of the building to the foot of the tower, using the angle of depression (45°):
- tan(45°) = Opposite/Adjacent = 10/d
- Since tan(45°) = 1, we get:
d = 10 m
2. Finding the height of the tower (H):
- Using the angle of elevation (60°) from the top of the building to the top of the tower:
- tan(60°) = (H - 10)/d
- Substituting d = 10 m and tan(60°) = √3 = 1.732:
- 1.732 = (H - 10) / 10
- H - 10 = 17.32
- H = 27.32 m
Final Calculation
The tower's height is approximately 27.3 m. Thus, the correct answer is option D (27.3 m).
This calculation demonstrates the application of trigonometric functions to solve real-world problems involving angles and distances.

Understanding the Problem
To find the length of the shadow cast by a man who is 180 cm tall with the sun at an angle of elevation of 60°, we can use basic trigonometry.
Setting Up the Triangle
- The height of the man (h) = 180 cm.
- The angle of elevation (θ) = 60°.
- The shadow length (s) = ?.
This forms a right triangle where:
- The height of the man is opposite to the angle of elevation.
- The shadow is adjacent to the angle.
Using Trigonometric Ratios
We can use the tangent function, which is defined as:
- tan(θ) = opposite/adjacent
In our case:
- tan(60°) = height of the man / length of the shadow.
Calculating the Length of the Shadow
Rearranging the formula gives:
- length of the shadow = height of the man / tan(60°).
Now, substituting the values:
- tan(60°) = √3 (approximately 1.732).
So:
- length of the shadow = 180 cm / √3.
Calculating this:
- length of the shadow = 180 cm / 1.732 ≈ 103.92 cm.
Conclusion
Thus, the length of the shadow of the man is approximately 103.92 cm, which corresponds to option 'C'.
This calculation illustrates the application of basic trigonometric principles to solve real-world problems involving angles and heights.

Understanding the Problem
The problem involves a man on a terrace observing a car. We need to determine the speed of the car based on angles of depression at two different times.
Given Data
- Initial distance from the car to the building: 200 m
- Initial angle of depression: 60°
- Angle of depression after 8 seconds: 30°
Calculating Heights and Distances
1. Initial Height Calculation:
- Using the angle of depression (60°):
- The height (h) of the terrace can be calculated using the tangent function:
- h = 200 * tan(60°) = 200 * √3
2. Position After 8 Seconds:
- After 8 seconds, the car makes an angle of depression of 30°:
- The new horizontal distance (d) from the building can be calculated:
- h = d * tan(30°)
- d = h / tan(30°) = (200 * √3) / (1/√3) = 600 m
Calculating the Distance Traveled by the Car
- Total Distance Covered:
- Initially, the car was 200 m away and is now 600 m away.
- Distance traveled = 600 m - 200 m = 400 m
Calculating Speed of the Car
- Speed Calculation:
- Speed = Distance / Time
- Speed = 400 m / 8 s = 50 m/s
Conclusion
The calculated speed of the car is incorrect in terms of the options provided. Therefore, if the answer is indeed stated as 16.67 m/s, it suggests a different interpretation or calculation might be needed. The correct approach leads to a clear understanding of the problem's requirements and the progression of the car's movement based on the angles of depression observed.

Understanding the Problem
We have two buildings: one taller (60 m) and one smaller. The angle of elevation from the top of the smaller building to the top of the taller building is 30 degrees, and the angle of depression from the top of the taller building to the foot of the smaller building is also 30 degrees.
Visualizing the Scenario
- Let the height of the smaller building be "h" meters.
- The height of the taller building is 60 m.
- The distance between the two buildings is "d" meters.
Using Trigonometry
1. Angle of Elevation (top of smaller to top of taller)
- From the top of the smaller building, the angle of elevation to the top of the taller building is 30 degrees:
- tan(30) = (60 - h) / d
- Therefore, d = (60 - h) * √3
2. Angle of Depression (top of taller to foot of smaller)
- From the top of the taller building, the angle of depression to the foot of the smaller building is also 30 degrees:
- tan(30) = h / d
- Thus, d = h * √3
Equating the Two Expressions for d
- (60 - h) * √3 = h * √3
Simplifying the Equation
- Dividing both sides by √3:
- 60 - h = h
- Rearranging gives:
- 60 = 2h
- h = 30 m
Conclusion
The height of the smaller building is 30 m. Therefore, the correct answer is option 'D'.