Trigonometry — NCERT Class 10: 18 MCQs

All 18 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 25 Quick Revision · 15

Warm-up · 6 questions

Q1. In a right triangle, $\sin A$ is defined as which ratio?

Beginner

A adjacent / hypotenuse

B opposite / hypotenuse

C opposite / adjacent

D hypotenuse / opposite

Answers and explanations are in the Veda app.

Q2. Which side of a right triangle is always the hypotenuse?

Beginner

A The shortest side

B The side opposite angle $A$

C The side opposite the right angle

D The side adjacent to angle $A$

Answers and explanations are in the Veda app.

Q3. What is $\cos 60^\circ$?

Beginner

A $1$

B $\frac{1}{\sqrt{2}}$

C $\frac{\sqrt{3}}{2}$

D $\frac{1}{2}$

Answers and explanations are in the Veda app.

Q4. What is $\tan 45^\circ$?

Beginner

A $0$

B $\sqrt{3}$

C $\frac{1}{\sqrt{3}}$

D $1$

Answers and explanations are in the Veda app.

Q5. A ladder leans against a wall making a $60^\circ$ angle with the ground. Which ratio connects the height reached on the wall to the ladder's length?

Beginner

A $\sin 60^\circ$

B $\cot 60^\circ$

C $\cos 60^\circ$

D $\tan 60^\circ$

Answers and explanations are in the Veda app.

Q6. Trigonometric ratios of an acute angle are independent of the size of the right triangle — they depend only on the angle, because all right triangles with the same acute angle are similar.

Beginner

A True

B False

Answers and explanations are in the Veda app.

Building up · 7 questions

Q7. In triangle $ABC$ right-angled at $B$, which ratio equals $\frac{BC}{AB}$?

Intermediate

A $\cos A$

B $\sin A$

C $\tan A$

D $\tan C$

Answers and explanations are in the Veda app.

Q8. If $\sin A = \frac{3}{5}$ for an acute angle $A$, what is $\cos A$?

Intermediate

A $\frac{4}{5}$

B $\frac{3}{4}$

C $\frac{5}{4}$

D $\frac{5}{3}$

Answers and explanations are in the Veda app.

Q9. Which identity is a direct restatement of Pythagoras' theorem divided by the square of the hypotenuse?

Intermediate

A $\sin^2 A + \cos^2 A = 1$

B $1 + \cot^2 A = \csc^2 A$

C $1 + \tan^2 A = \sec^2 A$

D $\tan A = \frac{\sin A}{\cos A}$

Answers and explanations are in the Veda app.

Q10. A student writes $\sin^2 30^\circ = \sin 900^\circ$. What is the correct value of $\sin^2 30^\circ$?

Intermediate

A $\frac{1}{2}$

B $1$

C $\frac{\sqrt{3}}{2}$

D $\frac{1}{4}$

Answers and explanations are in the Veda app.

Q11. In triangle $ABC$ right-angled at $B$, which statement is true?

Intermediate

A $\sin A = \sin C$

B $\sin A = \cos C$

C $\tan A = \tan C$

D $\cos A = \cos C$

Answers and explanations are in the Veda app.

Q12. Which of these is NOT a valid trigonometric identity?

Intermediate

A $1 + \tan^2 A = \sec^2 A$

B $1 + \cot^2 A = \csc^2 A$

C $\sin(A+B) = \sin A + \sin B$

D $\sin^2 A + \cos^2 A = 1$

Answers and explanations are in the Veda app.

Q13. An observer looks down from the top of a tower at a car on the ground. The angle between the horizontal and the line of sight is called the:

Intermediate

A angle of refraction

B angle of depression

C angle of incidence

D angle of elevation

Answers and explanations are in the Veda app.

Topper level · 5 questions

Q14. If $\tan A = \sqrt{3}$ for an acute angle $A$, what is $A$?

Advanced

A $45^\circ$

B $90^\circ$

C $60^\circ$

D $30^\circ$

Answers and explanations are in the Veda app.

Q15. A student's working gives $\sin A = 1.4$ for an acute angle $A$. What is the most likely error?

Advanced

A Opposite and hypotenuse were swapped or mislabelled

B The angle was measured in radians instead of degrees

C The identity $\sin^2 A + \cos^2 A = 1$ was applied incorrectly

D The triangle was not right-angled

Answers and explanations are in the Veda app.

Q16. If $\sec A = \frac{5}{3}$ for an acute angle $A$, what is $\tan A$?

Advanced

A $\frac{3}{4}$

B $\frac{5}{4}$

C $\frac{4}{3}$

D $\frac{3}{5}$

Answers and explanations are in the Veda app.

Q17. In triangle $ABC$, right-angled at $B$, if $\sin A = rac{3}{5}$, what is the value of $ an A$?

Advanced

A $rac{3}{4}$

B $rac{5}{3}$

C $rac{3}{2}$

D $rac{4}{3}$

Answers and explanations are in the Veda app.

Q18. A ladder leans against a wall making a $45^\circ$ angle with the ground. If the length of the ladder is $10$ meters, what is the height reached on the wall?

Advanced

A $5$ m

B $10$ m

C $7$ m

D $8$ m

Answers and explanations are in the Veda app.

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