How many practice questions are available for Trigonometry Introduction?

SparkEd Math offers 60+ practice questions for Trigonometry Introduction 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 Trigonometry Introduction content free on SparkEd Math?

Yes! All Trigonometry Introduction 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 Trigonometry Introduction differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Trigonometry Introduction 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 Trigonometry Introduction content aligned with the IB syllabus?

Yes, all Trigonometry Introduction questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Trigonometry Introduction — Class 9 IB (2025-26)

About Trigonometry Introduction — Class 9 IB

Define trigonometric ratios for right triangles and solve problems involving angles of elevation. This topic is part of the IB Class 9 mathematics syllabus (chapter: Unit 6). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 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.

Trigonometry Introduction — solved examples for Class 9 IB

Example 1easy

In a right-angled triangle PQR, right-angled at Q, if we consider angle P, which side is the 'opposite' side?

A)PQ
B)QR
C)PR
D)None of these

Step-by-step solution

Step 1: Identify the angle P in the right-angled triangle PQR.
Step 2: The side directly across from angle P is QR. Therefore, QR is the opposite side relative to angle P.

Answer: QR

Example 2medium

In a right-angled triangle PQR, right-angled at Q, which side is the 'adjacent' side to angle R?

A)A) PQ
B)B) QR
C)C) PR
D)D) None of these

Step-by-step solution

Identify the right angle, which is at Q. The hypotenuse is PR (the side opposite the right angle).
Consider angle R. The side opposite to angle R is PQ.
The side adjacent to angle R is QR, as it's next to angle R and is not the hypotenuse.

Answer: B) QR

Example 3hard

In a right-angled triangle PQR, right-angled at Q, PQ = 12 cm and QR = 5 cm. A point S is on PR such that QS is perpendicular to PR. Find the value of tan(∠PQS).

A)5/12
B)12/5
C)5/13
D)12/13

Step-by-step solution

First, find PR using the Pythagorean theorem: PR = √(PQ² + QR²) = √(12² + 5²) = √(144 + 25) = √169 = 13 cm.
In right triangle PQR, tan(∠P) = QR/PQ = 5/12.
In right triangle PQS, ∠PQS + ∠P + ∠QSP = 180°. Since ∠QSP = 90°, ∠PQS + ∠P = 90°. Thus, ∠PQS and ∠P are complementary angles.
Therefore, tan(∠PQS) = tan(90° - ∠P) = cot(∠P) = 1 / tan(∠P) = 1 / (5/12) = 12/5.

Answer: 12/5

Practice questions on Trigonometry Introduction

Q1.easy
A right-angled triangle ABC has sides AB = 5 cm, BC = 12 cm, and AC = 13 cm. If angle B is the right angle, what is the value of cos A?
1. A)5/13
2. B)12/13
3. C)5/12
4. D)12/5
Show answer
Answer: 5/13
Hint: Recall the definition of cosine: Adjacent / Hypotenuse. Identify the adjacent side and hypotenuse relative to angle A.
Q2.easy
A kite flyer wants to find the height of a kite (H) above the ground. The length of the string is 50 m, and the angle of elevation of the kite is 30°. Which trigonometric ratio should be used to find H?
1. A)sin 30° = H/50
2. B)cos 30° = H/50
3. C)tan 30° = H/50
4. D)sec 30° = H/50
Show answer
Answer: sin 30° = H/50
Hint: Consider the relationship between the angle of elevation, the height (opposite side), and the string length (hypotenuse).
Q3.easy
In a right-angled triangle, if angle X and angle Y are acute angles, and X + Y = 90°, which of the following statements is always true?
1. A)sin X = sin Y
2. B)cos X = tan Y
3. C)sin X = cos Y
4. D)tan X = 1
Show answer
Answer: sin X = cos Y
Hint: Remember the complementary angle identities. If two angles are complementary, how do their sine and cosine values relate?
Q4.medium
A right-angled triangle ABC has a right angle at B. If AB = 8 cm and BC = 6 cm, what is the value of tan C?
1. A)A) 6/10
2. B)B) 8/10
3. C)C) 6/8
4. D)D) 8/6
Show answer
Answer: D) 8/6
Hint: Recall the definition of tangent for an angle in a right triangle: tan(angle) = Opposite / Adjacent.
Q5.medium
For an acute angle A in a right-angled triangle, which of the following statements correctly defines a trigonometric ratio?
1. A)A) sin A = (Adjacent side) / (Hypotenuse)
2. B)B) tan A = (Opposite side) / (Hypotenuse)
3. C)C) cos A = (Adjacent side) / (Hypotenuse)
4. D)D) sec A = (Opposite side) / (Adjacent side)
Show answer
Answer: C) cos A = (Adjacent side) / (Hypotenuse)
Hint: Think about the SOH CAH TOA mnemonic. Each part corresponds to sine, cosine, or tangent.
Q6.medium
A vertical pole is 10 meters high. A wire is stretched from the top of the pole to a point on the ground, making an angle of 60° with the ground. What is the length of the wire?
1. A)A) 10√3 m
2. B)B) 20√3 / 3 m
3. C)C) 20 m
4. D)D) 10 m
Show answer
Answer: B) 20√3 / 3 m
Hint: Draw a right-angled triangle. Identify the known side (height of pole) as the opposite side to the given angle, and the unknown (wire length) as the hypotenuse. Which trigonometric ratio relates opposite and hypotenuse?
Q7.hard
For an acute angle θ (0° < θ < 90°), which of the following statements is NOT always true?
1. A)sin θ < 1
2. B)cos θ < 1
3. C)tan θ > sin θ
4. D)tan θ < 1
Show answer
Answer: tan θ < 1
Hint: Recall the definitions of sine, cosine, and tangent in a right triangle. Consider how their values change as the angle increases, especially near 45°.
Q8.hard
Rohan observes a tree 100 m away from his position. He measures the angle of elevation to the top of the tree as 30°. He calculates the height of the tree (h) using the formula tan 30° = h / 100. His friend Shreya points out a possible mistake in his calculation or setup. What is the most likely mistake Rohan might have made if his eye level is not at ground level?
1. A)He used the incorrect trigonometric ratio (should be sin or cos).
2. B)He did not consider his eye level height above the ground.
3. C)He assumed the tree was perfectly vertical.
4. D)He used an incorrect value for tan 30°.
Show answer
Answer: He did not consider his eye level height above the ground.
Hint: The angle of elevation is measured from the observer's horizontal line of sight. This horizontal line is at the observer's eye level, not necessarily the ground.
Q9.hard
A window in a building is 10 m above the ground. The angle of elevation of the top of a nearby tower from this window is 30°. The angle of depression of the base of the tower from the same window is 45°. Find the height of the tower.
1. A)10(1 + 1/√3) m
2. B)10(1 + √3) m
3. C)10(√3 - 1) m
4. D)10(√3 / (√3-1)) m
Show answer
Answer: 10(1 + 1/√3) m
Hint: Draw a diagram. The horizontal distance from the window to the tower base is common to both the elevation and depression triangles. Use this to find the parts of the tower's height.

These are 9 of the 59 questions available for Trigonometry Introduction. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.