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) cos2 θ + sin2θ, (ii) cos2 θ – sin2 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 tan2 45° + cos2 30° – sin2 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.