Height and Distance for SSC CGL, Attempt New Pattern Questions

SSC is increasing the difficulty level of questions and topics due to the increase in competition. Due to that, a lot of questions have been added from topics that were not part of the syllabus. It has been seen when Eduquity has conducted the SSC Stenographer and SSC Selection Post exams. Height and distance are one of the topics that have been seen in those exams. So our experts have decided that SSC can also ask questions about height and distance for SSC CGL 2025 Tier 1 exam. This blog has provided questions on height and distance, which match the level of the CGL exam with a basic concept. Along with that, we have provided some free preparation resources that will help you in your overall exam preparation.

Concept on Height and Distance for SSC CGL

Height and Distance problems deal with measuring the height of objects (like towers, buildings, trees, etc.) and the distance between two points using trigonometric concepts such as angles of elevation and angles of depression.

These problems are solved using basic right-angled triangle geometry and trigonometric ratios.

Key Trigonometric Ratios

Ratio	Formula
sin θ	Opposite / Hypotenuse
cos θ	Adjacent / Hypotenuse
tan θ	Opposite / Adjacent
cot θ	1 / tan θ
sec θ	1 / cos θ
cosec θ	1 / sin θ

Standard Trigonometric Values

Angle (θ)	sin θ	cos θ	tan θ
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	1/√2	1/√2	1
60°	√3/2	1/2	√3
90°	1	0	∞

Memorize these values—they’re essential for solving SSC CGL problems quickly.

Important Concepts and Formulas

1. Angle of Elevation: The angle formed between the line of sight and the horizontal when the observer looks upward.

2. Angle of Depression: The angle formed between the line of sight and the horizontal when the observer looks downward.

3. Right-Angled Triangle: Almost all height and distance problems form a right triangle, where:

• Vertical height = perpendicular
• Horizontal distance = base
• Line of sight = hypotenuse

4. Using Trigonometric Ratios:

• tan θ = Height / Distance
• Height = Distance × tan θ
• Distance = Height/tan θ

Questions on Height and Distance for SSC CGL: Free PDF

Here, we have provided the questions on height and distance for SSC CGL Tier 1 exam. Along with that, we have provided a PDF that consists of a detailed solution to these questions. You are advised to first understand the concept and formulas that we have provided above and then solve these questions.

Question 1: There are two hotels on opposite sides of a road. One of the hotels is 54 metres high and the angle of depression from top of this hotel to top and bottom of another hotel are 30^o and 60^o, respectively. Height of another hotel is:

A) 36√3 metres

B) 18√3 metres

C) 36 metres

D) 18 metres

Question 2: A person sitting on the top a hill observes that the angle of depression to a car (moving with a uniform speed) changes from 45^o to 60^o in 24 minutes. Find the time taken by the car to reach the bottom of the hill from the point where angle of depression was 60^o.

A) 24(√3 – 1) minutes

B) 12(√3 + 1) minutes

C) 24(√3 + 1) minutes

D) 12(√3 – 1) minutes

Question 3: If the angle of depression from the Sun to top of a pole changes from 30^o to 45^o, then the length of the shadow of a pole decreases by 40 metres. Find the height of the pole.

A) 10(√3 + 1) metres

B) 40(√3 + 1) metres

C) 20(√3 + 1) metres

D) 20√3 metres

Question 4: A pole is bent at a point above the ground above due to storm. Its top meets the ground at a distance of 12√3 metres from its foot and makes an angle of 30^o with the ground. Find the original height of the pole.

A) 36 metres

B) 32 metres

C) 28 metres

D) 40 metres

Question 5: A person observes that the angle of elevation to the top of a pole of height 12 metres is 30^o. Find the distance of the person from the foot of the pole.

A) 4√3 metres

B) 12(√3 + 1) metres

C) 15 metres

D) 12√3 metres

Question 6: 144 meter from the foot of a cliff on level of ground, the angle of elevation of the top of cliff is 30^o. The height (in metres) of this cliff:

A) 32√3

B) 64√3

C) 48√3

D) 54√3

Question 7: A ladder is leaning against a wall makes an angle ‘x’ with the horizontal ground such that tanx = 192/80. If the length of the ladder is 52 metres, then what is the distance (in metres) of the foot of the ladder from the wall?

A) 20 metres

B) 15 metres

C) 30 metres

D) 40 metres

Question 8: From a point ‘P’, which is180 metres away from the foot of the fort, the angle of elevation to the top of the fort is ‘x’ such that secx = 13/12. Find the height of the fort.

A) 75 metres

B) 120 metres

C) 100 metres

D) 60 metres

Question 9: The angle of elevation to the top of a tree from two points on either of its two sides is 30^o and 60^o, respectively. If these two points of observation are 800 metres apart, then find the height of the tree.

A) 150√3 metres

B) 200√3 metres

C) 150(√3 + 1) metres

D) None of these

Question 10: The shadow of a vertical tree increases by 15 metres when the altitude of sun changes from 45^o to 30^o. Find the height of the tree.

A) 30(√2 – 1)/2

B) 15(√3 + 1)/2

C) 30√(3 + 1)/2

D) 5(√2 – 1)

Tips and Tricks to Solve Height and Distance Questions in SSC CGL Exam

Here we have provided the tips and tricks that will help you solve height and distance questions in SSC CGL exam easily. Follow these tips when you practice for these questions and boost your preparation level.

• Draw a Diagram for Easy Visualization: Before solving the question, draw a neat right-angled triangle based on the problem. Label its height (perpendicular), base (distance), and hypotenuse (line of sight). Mark the angle of elevation or depression clearly. This will help you to avoid mistakes.
• Memorize Standard Trigonometric Ratios: There is a use of values for sin, cos, tan, etc, for different angles. Keeping these values in mind can help you solve questions in less time. Most questions of the SSC will be asked based on these values.
• Understand the Difference Between Elevation and Depression: The Direction of the angle matters in solving the questions.
  • Angle of elevation: Looking upward.
  • Angle of depression: Looking downward.
• Use Pythagoras’ Theorem: There will be some problems where you need to find the hypotenuse. In that case, use the height and distance formula.
  • Hypotenuse²=Height²+Distance²
• Be Careful With Units: Make sure that you have converted the units to the same parameters. If you are using a meter, then first convert all values to meters.
• Practice Reverse Problems: Sometimes you’re given the height and need to find the angle. In that case, use the inverse trigonometric function:

Additional Resources for SSC CGL 2025 Exam Preparation

Have you prepared the Height and Distance for SSC CGL with practice (questions are provided in this blog)? If yes, now it’s time to practice other topics under time conditions that match the level of the SSC CGL. For that, we have provided free resources such as topic-wise tests, full-length mock tests, previous year question papers, and others. Click on the links given below and boost your preparation.

Click for Mock Test ->	SSC CGL Free Full-Length Mock Test
Click for SSC CA ->	SSC CGL Free Weekly Current Affairs Tests
Click for Quant ->	Quantitative Aptitude Free Topic Tests
Click for Reasoning ->	General Reasoning Free Topic Tests
Click for English ->	English Comprehension Free Topic Tests
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Click for Sectional Mock Tests ->	SSC CGL Free Sectional Mock Tests
Click for PYQs ->	Free SSC CGL Previous Year Question Papers

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Height and Distance for SSC CGL: FAQs