With sin 30° equal to 1/2 and tan 45° equal to 1, this Class 10 sheet opens with two standard angles as ratios. The sine ratio opposite ÷ hypotenuse and the answer 4/5 appear among the later rows of the ratio table.
Key Takeaways
sin 30° = 1/2 (Q1).
tan 45° = 1 (Q2).
Q3 records opposite ÷ hypotenuse for the sine ratio.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The value of sin 30° is
(a) 0(b) 1(c) 1/2(d) √3/2
2.The value of tan 45° is
(a) 0(b) 1/2(c) 1(d) √3
3.In a right triangle ABC, right-angled at B, the ratio sin A is equal to
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the values of sin 0° and cos 0°.
8.In a right triangle, the side opposite to angle A is 3 units and the hypotenuse is 5 units. Find sin A.
9.Express tan A in terms of sin A and cos A.
10.Find the value of sin 30° + cos 60°.
11.If tan A = 1 and A is an acute angle, find the value of A.
12.Write the value of cot 45°.
13.Find the value of sin 45° + cos 45°.
14.If cos A = 4/5, find the values of sin A and tan A.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A ladder 13 m long rests against a vertical wall with its foot 5 m away from the wall. Find the height at which the top of the ladder touches the wall.
16.A kite is flying at a height of 30 m and the length of the string is 60 m. Find the angle the string makes with the ground.
17.The shadow of a tower is exactly equal to its height. Find the angle of elevation of the sun.
18.A tree 15 m tall casts a shadow of length 15√3 m. Find the angle of elevation of the sun.
19.An observer sees the top of a pole at an angle of elevation of 60°. If the pole is 20√3 m tall, find the distance of the observer from the foot of the pole.
20.A boy walks 12 m towards the north and then 5 m towards the east. Find the straight-line distance of his final position from the starting point.
Answer Key
1. c) 1/2
2. c) 1
3. a) opposite / hypotenuse
4. b) 1
5. a) 4/5
6. c) 2
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the value of sin 30°?
1/2, option (c) in this worksheet (Q1).
What is the value of tan 45°?
1, option (c) in this worksheet (Q2).
Which ratio defines sine?
opposite ÷ hypotenuse, option (a) in this worksheet (Q3).
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