How many practice questions are available for Trigonometric Ratios?

SparkEd Math offers 60+ practice questions for Trigonometric Ratios across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Trigonometric Ratios content free on SparkEd Math?

Yes! All Trigonometric Ratios content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Trigonometric Ratios differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Trigonometric Ratios problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Trigonometric Ratios content aligned with the ICSE syllabus?

Yes, all Trigonometric Ratios questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Trigonometric Ratios — Class 9 ICSE (2025-26)

About Trigonometric Ratios — Class 9 ICSE

Define sine, cosine, and tangent ratios and solve problems involving right triangles. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 15). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Trigonometric Ratios

Introduction to Trigonometric Ratios: Relating Sides and Angles
The Fundamental Trigonometric Ratios: Sine, Cosine, and Tangent
Applying Trigonometric Ratios: Finding Unknown Sides
Finding Unknown Angles and Special Angles
Summary, Connections, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Trigonometric Ratios — solved examples for Class 9 ICSE

Example 1easy

In a right-angled triangle ABC, right-angled at B, if AC is the hypotenuse, which side is opposite to angle C?

A)AB
B)BC
C)AC
D)Cannot be determined

Step-by-step solution

Identify the angle in question: angle C.
Identify the vertex of angle C. The sides forming angle C are BC and AC.
The side that is not touching vertex C is AB. Therefore, AB is opposite to angle C.

Answer: AB

Example 2medium

In a right-angled triangle ABC, right-angled at B, if AB = 7 cm and BC = 24 cm, what is the value of sin C?

A)7/25
B)24/25
C)7/24
D)24/7

Step-by-step solution

Given AB = 7 cm, BC = 24 cm. In right-angled ΔABC, by Pythagoras theorem, AC² = AB² + BC².
AC² = 7² + 24² = 49 + 576 = 625.
$AC = √625 = 25 cm.$
For angle C, the opposite side is AB and the hypotenuse is AC. sin C = Opposite/Hypotenuse.
$sin C = AB/AC = 7/25.$

Answer: 7/25

Example 3hard

In a right-angled triangle ABC, right-angled at B, AB = 7 cm and AC - BC = 1 cm. What is the value of (sec A + cot C) / (tan C - cosec A)?

A)-7/3
B)-14/3
C)-28/3
D)-7

Step-by-step solution

Let BC = x. Then AC = x + 1. In ΔABC, by Pythagoras theorem: AB² + BC² = AC².
7² + x² = (x + 1)² => 49 + x² = x² + 2x + 1 => 48 = 2x => x = 24 cm. So, BC = 24 cm and AC = 25 cm.
For angle A: sec A = Hyp/Adj = AC/AB = 25/7. For angle C: cot C = Adj/Opp = BC/AB = 24/7. So, (sec A + cot C) = (25/7) + (24/7) = 49/7 = 7.
For angle C: tan C = Opp/Adj = AB/BC = 7/24. For angle A: cosec A = Hyp/Opp = AC/BC = 25/24. So, (tan C - cosec A) = (7/24) - (25/24) = -18/24 = -3/4. Therefore, (sec A + cot C) / (tan C - cosec A) = 7 / (-3/4) = -28/3.

Answer: -28/3

Practice questions on Trigonometric Ratios

Q1.easy
Consider a right-angled triangle PQR, right-angled at Q. If PQ = 5 cm and QR = 12 cm, what is the value of sin P?
1. A)5/13
2. B)12/13
3. C)5/12
4. D)12/5
Show answer
Answer: 12/13
Hint: Remember that sine is the ratio of the side opposite to the angle to the hypotenuse. You might need Pythagoras' theorem first.
Q2.easy
Which of the following statements correctly defines tan A in a right-angled triangle, where A is an acute angle?
1. A)tan A = Opposite side / Hypotenuse
2. B)tan A = Adjacent side / Hypotenuse
3. C)tan A = Opposite side / Adjacent side
4. D)tan A = Hypotenuse / Opposite side
Show answer
Answer: tan A = Opposite side / Adjacent side
Hint: Recall the SOH CAH TOA mnemonic to remember the definitions of sine, cosine, and tangent.
Q3.easy
If sin θ = 3/5 in a right-angled triangle, what is the value of cosec θ?
1. A)3/5
2. B)5/3
3. C)4/5
4. D)5/4
Show answer
Answer: 5/3
Hint: Cosecant is one of the reciprocal trigonometric ratios. Think about which ratio it reciprocates.
Q4.medium
A ladder 13 meters long leans against a vertical wall. If the base of the ladder is 5 meters away from the wall, what is the cosine of the angle the ladder makes with the ground?
1. A)5/13
2. B)12/13
3. C)5/12
4. D)13/5
Show answer
Answer: 5/13
Hint: Draw a right-angled triangle representing the wall, ground, and ladder. Identify the hypotenuse and the side adjacent to the angle with the ground.
Q5.medium
Which of the following statements is TRUE for an acute angle A in a right-angled triangle?
1. A)sin A can be greater than 1
2. B)cos A can be greater than 1
3. C)tan A can be greater than 1
4. D)sin A = 1.5
Show answer
Answer: tan A can be greater than 1
Hint: Recall the definitions of sine, cosine, and tangent. Think about the relative lengths of the sides involved in each ratio compared to the hypotenuse.
Q6.medium
In ΔPQR, right-angled at Q, if sin P = 8/17 and the hypotenuse PR = 51 cm, what is the length of the side QR?
1. A)15 cm
2. B)24 cm
3. C)30 cm
4. D)36 cm
Show answer
Answer: 24 cm
Hint: Use the definition of sin P. Remember that sin P = Opposite side / Hypotenuse.
Q7.hard
If tan θ = (m² - n²) / (2mn), where θ is an acute angle, find the value of (sec θ + tan θ).
1. A)n/m
2. B)m/n
3. C)(m²+n²)/(2mn)
4. D)(m²-n²)/(m²+n²)
Show answer
Answer: m/n
Hint: Draw a right-angled triangle and label the opposite and adjacent sides using the given tan θ. Use the Pythagorean theorem to find the hypotenuse in terms of m and n.
Q8.hard
For any acute angle A in a right-angled triangle, which of the following statements must always be true?
1. A)sin A > 1
2. B)tan A < 1
3. C)sec A < 1
4. D)cos A ≤ 1
Show answer
Answer: cos A ≤ 1
Hint: Recall the definitions of the trigonometric ratios and the relationship between the sides of a right-angled triangle, especially the hypotenuse.
Q9.hard
In triangle ABC, AD is perpendicular to BC. If AB = 13 cm, AC = 15 cm, and BD = 5 cm, find the value of tan C.
1. A)4/3
2. B)3/4
3. C)12/5
4. D)5/12
Show answer
Answer: 4/3
Hint: Identify the two right-angled triangles formed by the altitude AD. Use the Pythagorean theorem in the first triangle to find AD, then use AD in the second triangle to find CD.

These are 9 of the 60 questions available for Trigonometric Ratios. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.