# MATH – TEST 1 – CHAPTER 8 & 9 Trigonometry

**NEUTRON CLASSES**

**CLASS – X**

**MATH – TEST 1 – CHAPTER 8 & 9**

**Q.1**. Given tan A = 4/3, find the other trigonometric ratios of the angle A.

**Q. 2**. Consider ∆ ACB, right-angled at C, in which AB = 29 units, BC = 21 units and ∠ ABC = θ.

Determine the values of (i) cos^{2} θ + sin^{2}θ, (ii) cos^{2 }θ – sin^{2 }θ.

**Q. 3**. Given 15 cot A = 8, find sin A and sec A.

**Q. 4**. In ∆ PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠ QPR and ∠ PRQ.

**Q. 5**. If sin (A – B) = 1/2, cos (A + B) = 1/2, 0° < A + B ≤ 90°, A > B, find A and B.

**Q. 6**. Find. 2 tan^{2} 45° + cos^{2} 30° – sin^{2} 60°.

**Q. 7**. If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.

**Q. 8**. Prove that sec A (1 – sin A)(sec A + tan A) = 1.

**Q. 9**. A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.

**Q. 10**. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P.