Trigonometry Class 10 Important Questions to Score 5 Marks Easily

Trigonometry is one of the most important chapters in Class 10 Maths because it helps students connect angles, sides, and right triangles in a very practical way. In board exams, trigonometry is highly important not only because direct ratio-based questions are asked, but also because application-based questions from heights and distances are very common. These are often the questions that carry 5 marks and can improve the final score quickly.

Many students feel nervous about trigonometry because they think the chapter is only about memorising formulas. In reality, this chapter becomes much easier when students remember a few key trigonometric values, understand the meaning of angle of elevation and angle of depression, and learn how to draw a clean diagram before solving the question.

At Deeksha Vedantu, we always encourage students to approach trigonometry step by step. First remember the important trigonometric values, then understand the angle-based terms, then draw the diagram carefully, and only after that apply the correct ratio. This simple method makes 5-mark questions much easier to solve.

Why Trigonometry Is Important in Class 10

Trigonometry is an important scoring chapter because it appears repeatedly in board exams and often gives students a chance to secure marks through clear steps.

Why Students Should Prepare This Chapter Well

• it is a regular board-exam chapter
• it includes direct value-based questions
• it includes heights and distances problems
• it helps students score full marks in 5-mark questions
• it improves diagram-based reasoning and stepwise presentation

Chapter Overview at a Glance

This quick table helps students revise the full chapter faster.

Quick Concept Table

What Is Trigonometry in Class 10

Trigonometry is the branch of mathematics that studies the relationship between angles and sides of a right triangle.

In Class 10, students mostly use trigonometric ratios to solve angle-based and height-distance questions.

Most Important Trigonometric Ratios to Remember

Before solving application questions, students should revise the key values carefully.

tan Values Table

These three values are extremely important because many board questions from application of trigonometry are solved directly using tan 30°, tan 45°, or tan 60°.

Other Important Trigonometric Values

Although tan values are especially useful in many board questions, students should also remember the values of sin and cos.

sin Values Table

cos Values Table

How to Choose the Correct Trigonometric Ratio

Students often know the values but still choose the wrong ratio.

Ratio Selection Table

In application-based board questions, tan θ is often the most useful because height and horizontal distance are usually given or required.

Why tan Is Frequently Used in 5-Mark Questions

In many application-based questions, students are asked to relate height and horizontal distance.

Key Reason

When the relation involves perpendicular and base, tan θ is the most useful ratio.

Because:

tan θ = perpendicular/base

This is why tan 30°, tan 45°, and tan 60° play a major role in board questions.

Angle of Elevation and Angle of Depression

These two terms are among the most important concepts in application of trigonometry.

Case 1: Angle of Elevation

When an observer looks upward at an object placed above the eye level, the angle formed between the horizontal line and the line of sight is called the angle of elevation.

Important Position Rule

The angle of elevation is always below the line of sight.

Example Situation

A person standing on the ground looks at the top of a tower. The angle between the ground line and the line of sight is the angle of elevation.

Case 2: Angle of Depression

When an observer looks downward at an object below the eye level, the angle formed between the horizontal line and the line of sight is called the angle of depression.

Important Position Rule

The angle of depression is always above the line of sight.

Example Situation

A person standing on the top of a building looks down at a car on the road. The angle between the horizontal line from the observer and the line of sight is the angle of depression.

Elevation vs Depression Table

Why Students Must Draw the Diagram First

This is one of the most important rules for solving trigonometry word problems.

Correct Solving Habit

• read the question slowly
• identify all given values
• draw the diagram neatly
• mark the angle properly
• identify the right triangle
• apply the suitable trigonometric ratio

If students skip the diagram and start solving immediately, mistakes become much more likely.

Why the Right Triangle Is So Important

All the basic trigonometric ratios in Class 10 are applied in a right triangle.

Main Idea

Once the right triangle is clearly visible in the figure, students can identify:

• perpendicular
• base
• hypotenuse

and then choose the correct ratio such as sin, cos, or tan.

Step-by-Step Method to Solve Heights and Distances Questions

This is the safest method for board exams.

Solving Strategy Table

Important Question 1: Angle of Depression from a Tower

The angle of depression of a car standing on the ground from the top of a 75 m high tower is 30°. Find the distance of the car from the base of the tower.

Given

• height of tower = 75 m
• angle of depression = 30°
• required distance from the base = x m

Step 1

Since the horizontal line at the top is parallel to the ground, the angle of elevation from the car to the top of the tower is also 30°.

Step 2

Form a right triangle with:

• perpendicular = 75 m
• base = x m
• angle = 30°

Step 3

Apply tan 30°:

1/√3 = 75/x

Step 4

Solve for x:

x = 75√3

Answer

The distance of the car from the base of the tower is 75√3 m.

Important Question 2: Shadow of a Tower

The shadow of a tower standing on a level plane is found to be 50 m longer when the sun’s elevation is 30° than when it is 60°. Find the height of the tower.

Given

• longer shadow = x + 50 m
• shorter shadow = x m
• height of tower = h m

Step 1

For the angle 60°:

tan 60° = h/x

√3 = h/x

h = x√3

Step 2

For the angle 30°:

tan 30° = h/(x + 50)

1/√3 = h/(x + 50)

h = (x + 50)/√3

Step 3

Equate both expressions of h:

x√3 = (x + 50)/√3

Multiply both sides by √3:

3x = x + 50

Step 4

Solve:

2x = 50

x = 25

Then:

h = x√3 = 25√3

Answer

The height of the tower is 25√3 m.

Important Question 3: Observer Moving Toward a Tower

From a point on the ground, the angle of elevation of the top of a tower is 30°. After moving 20 m toward the tower, the angle of elevation becomes 60°. Find the height of the tower.

Given

• first angle = 30°
• second angle = 60°
• distance moved toward the tower = 20 m
• height of tower = h m

Step 1

Let the distance from the second point to the tower be x m.

Then the first point is x + 20 m away.

Step 2

Using the first position:

tan 30° = h/(x + 20)

1/√3 = h/(x + 20)

h = (x + 20)/√3

Step 3

Using the second position:

tan 60° = h/x

√3 = h/x

h = x√3

Step 4

Equate both values of h:

(x + 20)/√3 = x√3

x + 20 = 3x

20 = 2x

x = 10

Then:

h = 10√3

Answer

The height of the tower is 10√3 m.

Important Question 4: Ladder Against a Wall

A ladder is placed against a wall making an angle of 60° with the ground. If the foot of the ladder is 6 m away from the wall, find the length of the ladder and the height reached on the wall.

Given

• base = 6 m
• angle with ground = 60°
• ladder length = l m
• wall height = h m

Step 1

Use cos 60° to find the ladder length:

cos 60° = base/hypotenuse

1/2 = 6/l

Step 2

Solve for l:

l = 12 m

Step 3

Use sin 60° to find the height on the wall:

sin 60° = h/12

√3/2 = h/12

Step 4

Solve for h:

h = 6√3 m

Answer

• ladder length = 12 m
• height reached on the wall = 6√3 m

Important Question 5: Pole and Rope Problem

A pole is supported by a rope tied from its top to a point on the ground. If the rope makes an angle of 45° with the ground and the distance of the point from the pole is 12 m, find the height of the pole.

Given

• base = 12 m
• angle = 45°
• height of pole = h m

Step 1

Apply tan 45°:

tan 45° = h/12

Step 2

Use tan 45° = 1:

1 = h/12

Step 3

Solve:

h = 12 m

Answer

The height of the pole is 12 m.

Important Question 6: Building and Observer Height Difference

From the top of a 20 m high building, the angle of depression of the top of another building is 30°. If the horizontal distance between the buildings is 10√3 m, find the height of the second building.

Given

• height of first building = 20 m
• horizontal distance = 10√3 m
• angle of depression = 30°
• height of second building = h m

Step 1

The difference in heights is:

20 – h

Step 2

Use the angle of depression and the corresponding angle of elevation:

tan 30° = (20 – h)/(10√3)

Step 3

Substitute tan 30° = 1/√3:

1/√3 = (20 – h)/(10√3)

Step 4

Solve:

10 = 20 – h

h = 10

Answer

The height of the second building is 10 m.

Important Board Question Patterns from Trigonometry

Board exams often repeat certain important patterns from this chapter.

Case 1: Direct Ratio-Based Question

Students are asked to use standard trigonometric values directly.

Case 2: Angle of Elevation Question

These involve looking upward from the ground to the top of an object.

Case 3: Angle of Depression Question

These involve looking downward from a height to an object below.

Case 4: Shadow and Sun Elevation Question

These are among the most common 5-mark questions.

Case 5: Observer Movement Question

These involve two different positions and two different angles.

Case 6: Ladder, Pole, and Rope Questions

These involve right triangle formation and use of sin, cos, or tan.

Board Pattern Summary Table

Common Mistakes Students Make in Application of Trigonometry

These mistakes are very common in board exams.

Common Mistakes Table

Quick Revision Sheet for 5-Mark Trigonometry Questions

This section is useful before board exams.

Must-Remember Values Table

Angle Terms Table

Ratio Use Table

Best Strategy to Score 5 Marks Easily in Trigonometry

This chapter becomes much easier when students follow a disciplined method.

Step-by-Step Revision Table

Practice Questions

This section helps students revise through standard board-style patterns.

Important Practice Questions

1. The angle of elevation of the top of a tower from a point on the ground is 30°. If the tower is 40 m high, find the distance of the point from the tower.
2. The shadow of a pole is 20 m long when the angle of elevation of the sun is 45°. Find the height of the pole.
3. A ladder makes an angle of 60° with the ground. If the foot of the ladder is 5 m away from the wall, find the length of the ladder.
4. From the top of a 30 m building, the angle of depression of a car is 45°. Find the distance of the car from the base of the building.
5. From a point 15 m away from a tower, the angle of elevation of its top is 60°. Find the height of the tower.

FAQs

Q1. What is the most important concept in application of trigonometry?

The most important concept is drawing the diagram correctly and identifying the right triangle.

Q2. What is angle of elevation?

It is the angle formed between the horizontal and the line of sight when the observer looks upward.

Q3. What is angle of depression?

It is the angle formed between the horizontal and the line of sight when the observer looks downward.

Q4. Which trigonometric ratio is used most in board questions?

Tan θ is used very often because many questions involve height and horizontal distance.

Q5. Why are tan 30°, tan 45°, and tan 60° so important?

These values appear very frequently in Class 10 board-level application questions.

Q6. How do I know whether to use sin, cos, or tan?

Choose the ratio based on which sides are involved: perpendicular-hypotenuse for sin, base-hypotenuse for cos, and perpendicular-base for tan.

Q7. Why do students lose marks in trigonometry word problems?

Students usually lose marks because of poor diagram drawing, confusion between elevation and depression, or wrong ratio selection.

Q8. How can I score full marks in 5-mark trigonometry questions?

You can score full marks by remembering the key values, drawing the diagram properly, choosing the correct ratio, and writing the steps clearly.

Conclusion

Trigonometry in Class 10 becomes much easier when students focus on the basics that really matter: trigonometric values, angle of elevation, angle of depression, and neat diagram-based solving. Most 5-mark questions are not difficult if the figure is understood correctly and the right ratio is applied with patience.

The best way to prepare this chapter is to revise tan 30°, tan 45°, and tan 60° regularly, practise drawing diagrams, and solve application-based questions step by step. At Deeksha Vedantu, we always remind students that in trigonometry, a clean diagram and a calm approach can turn a difficult-looking question into an easy full-mark answer.