Trigonometric Ratios (Acute Angle) MCQs Quiz | Class 10
This quiz is designed for **Class X** students studying **Mathematics (Code 041)**, specifically **Unit V: Trigonometry**, focusing on **Trigonometric Ratios (Acute Angle)**. It covers fundamental concepts of sin, cos, tan, cot, sec, and cosec in a right-angled triangle. Test your knowledge by attempting all 10 multiple-choice questions, then submit to see your score and download a detailed PDF answer sheet for review.
Understanding Trigonometric Ratios for Acute Angles
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. In Class 10, we primarily focus on right-angled triangles and the ratios of their sides with respect to acute angles. These ratios are fundamental to solving problems involving heights, distances, and angles in various real-world scenarios.
Key Trigonometric Ratios
For a right-angled triangle, consider an acute angle ‘A’.
- Sine of angle A (sin A): Ratio of the side opposite to angle A to the hypotenuse.
- Cosine of angle A (cos A): Ratio of the side adjacent to angle A to the hypotenuse.
- Tangent of angle A (tan A): Ratio of the side opposite to angle A to the side adjacent to angle A.
A common mnemonic to remember these is SOH CAH TOA:
- SOH: Sin = Opposite / Hypotenuse
- CAH: Cos = Adjacent / Hypotenuse
- TOA: Tan = Opposite / Adjacent
Reciprocal Ratios
In addition to the primary ratios, there are three reciprocal ratios:
- Cosecant of angle A (cosec A): Reciprocal of sin A. (Hypotenuse / Opposite)
- Secant of angle A (sec A): Reciprocal of cos A. (Hypotenuse / Adjacent)
- Cotangent of angle A (cot A): Reciprocal of tan A. (Adjacent / Opposite)
These relationships are important:
- cosec A = 1 / sin A
- sec A = 1 / cos A
- cot A = 1 / tan A
Important Points to Remember
- The trigonometric ratios are dimensionless numbers.
- The values of sin A and cos A are always less than or equal to 1.
- The values of sec A and cosec A are always greater than or equal to 1.
- The values of tan A and cot A can be any positive real number for acute angles.
- The values of trigonometric ratios for specific angles (0, 30, 45, 60, 90 degrees) are fixed and should be memorized.
Practice Questions (without options)
- In a right triangle ABC, right-angled at B, if AB = 8 cm and BC = 15 cm, find sin A.
- If cos P = 3/5, find tan P.
- Given tan theta = 4/3, find the value of (sin theta + cos theta).
- If sin A = 1/2, calculate the value of (3 sin A – 4 sin cube A).
- In triangle PQR, right-angled at Q, PQ = 7 cm and PR = 25 cm. Determine the value of tan P – tan R.
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.