CBSE Class 10 · Mathematics · Chapter 9
Class 10 Maths: Some Applications of Trigonometry Quiz
Concept & Application Quiz — 25 questions to test what you really know.
This quiz is built for CBSE Class 10 students studying Chapter 9, Some Applications of Trigonometry. It checks your understanding of the angle of elevation, the angle of depression, the line of sight, and real-world heights-and-distances problems involving towers, ladders, kites, shadows, and buildings. Answer all 25 questions to see instant explanations and your final score.
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Full Quiz Transcript: All 25 Questions & Answers
Prefer to read through everything at once? Every question below is answered and explained in plain text, ideal for quick revision before an exam.
Q1. What is the line segment connecting an observer's eye to the point being viewed called?
The line of sight — the straight line drawn from the observer's eye to the point on the object being viewed.
Q2. What is the angle formed with the horizontal when an observer looks up at an object above eye level called?
The angle of elevation — formed when the observed point is above the horizontal level, requiring the observer to raise their head.
Q3. What is the angle formed when an observer looks down at an object below eye level called?
The angle of depression — formed when the line of sight is below the horizontal level, as when looking down from a balcony at an object on the ground.
Q4. Which trigonometric ratio is most useful for finding a building's height when the distance to its base and the angle of elevation are known?
tan(theta), since tangent equals the opposite side (height) divided by the adjacent side (distance), giving the height directly without needing the hypotenuse.
Q5. A tower's angle of elevation is 60 degrees from a point 15 m from its base. What is the tower's height?
15 times the square root of 3 meters, approximately 25.98 m, using tan 60 degrees = height / 15.
Q6. An electrician must reach a point 1.3 m below the top of a 5 m pole. How high must the ladder reach from the base?
3.7 meters (5 m minus the 1.3 m clearance from the top).
Q7. A 1.5 m tall observer stands 28.5 m from a chimney, with a 45-degree angle of elevation to its top. What is the chimney's total height?
30 meters (28.5 m above eye level, since tan 45 degrees equals 1, plus the observer's own height of 1.5 m).
Q8. For a building 10 m tall viewed at a 30-degree angle of elevation from a point P, which equation finds the distance AP?
tan 30 degrees = 10 / AP, since tangent equals the height (opposite side) divided by the distance (adjacent side).
Q9. If a tower's shadow is 40 m longer at a 30-degree sun angle than at 60 degrees, and x is the shorter shadow, what is the shadow length at 30 degrees?
x + 40, since the shadow at the smaller angle (30 degrees) is longer by 40 m.
Q10. From a multi-storeyed building, the angle of depression to the bottom of an 8 m building is 45 degrees. If H is the taller building's height and y is the distance between them, what does this tell us?
H = y, because tan 45 degrees equals 1, so the height must equal the horizontal distance.
Q11. From a bridge 3 m above a river, the angles of depression to the two banks are 30 and 45 degrees. How do you find the river's width?
Add the two horizontal distances calculated from the bridge to each bank, since the banks lie on opposite sides of the point directly below the bridge.
Q12. A circus artist climbs a 20 m rope tied from a pole's top to the ground at 30 degrees. Which equation gives the pole's height, h?
sin 30 degrees = h / 20, since sine equals the opposite side (height) divided by the hypotenuse (rope length).
Q13. A tree breaks in a storm and its top touches the ground 8 m from the foot at a 30-degree angle. What makes up the tree's total original height?
The sum of the standing vertical part and the broken part, which forms the hypotenuse of the triangle.
Q14. A kite flies at 60 m height with its string inclined at 60 degrees. What is the string's length?
40 times the square root of 3 meters, approximately 69.28 m, from sin 60 degrees = 60 / L.
Q15. A 1.5 m tall boy watches a 30 m building as the angle of elevation increases from 30 to 60 degrees. What height should be used in the calculation?
28.5 meters, the building's height minus the boy's own height, since the angle is measured from his eyes.
Q16. A transmission tower sits on a 20 m building. The angles of elevation to the building's bottom and the tower's top are 45 and 60 degrees. What is the tower's height alone?
20 times (the square root of 3 minus 1) meters, approximately 14.64 m.
Q17. A 1.6 m statue stands on a pedestal, with elevation angles of 60 degrees to the statue top and 45 degrees to the pedestal top. If h is the pedestal height and d the distance, which equation applies?
h = d, since tan 45 degrees equals 1 for the pedestal's own triangle.
Q18. A 50 m tower and a building have mutual elevation angles of 30 and 60 degrees. What must be found first to get the building's height?
The horizontal distance between the tower and the building, since it is shared by both right triangles.
Q19. Two equal poles stand on either side of an 80 m road. If the distance to one pole from a point between them is x, what is the distance to the other?
80 minus x, since both distances must add up to the total road width of 80 m.
Q20. From a 7 m building, the angle of elevation to a cable tower's top is 60 degrees and the angle of depression to its foot is 45 degrees. What is the horizontal distance to the tower?
7 meters, since tan 45 degrees equals 1, making the horizontal distance equal to the building's height.
Q21. From a 75 m lighthouse, two ships are seen at 30 and 45 degree angles of depression. What is the distance to the closer ship?
75 meters, since the ship with the larger angle of depression (45 degrees) is closer, and tan 45 degrees equals 1.
Q22. A balloon at 88.2 m is viewed by a 1.2 m tall girl as the angle changes from 60 to 30 degrees. What height should be used in the calculation?
87 meters, the balloon's height minus the girl's own height.
Q23. A car's angle of depression from a tower changes from 30 to 60 degrees. What does this indicate about the car's movement?
The car is moving toward the tower, since an increasing angle of depression means the object is getting closer to the base.
Q24. What condition must be met for an angle of elevation to be formed?
The object being viewed must be above the horizontal level, requiring the observer to raise their head to see it.
Q25. According to the chapter, what can be determined using trigonometric ratios?
The height or length of an object, or the distance between two distant objects.
