Class 10 • Maths • Chapter 9
SOME APPLICATIONS OF TRIGONOMETRY
True & False Quiz
Heights. Distances. Angles.
✓True
✗False
25
Questions
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Ch.9
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Why True & False for SOME APPLICATIONS OF TRIGONOMETRY?
How this format sharpens your conceptual clarity
🔵 This chapter applies trigonometry to real measurement problems — finding heights of towers, widths of rivers, and distances to objects.
✅ T/F questions test the definitions of angle of elevation vs depression and the correct application of tan formula.
🎯 Angle of elevation = angle of depression (alternate interior angles when observer and object are at equal heights) — a tricky but examinable T/F.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The chapter “Some Applications of Trigonometry” mainly deals with problems on heights and distances.
Q 2
In this chapter, angles are always measured in radians.
Q 3
The line joining the observer’s eye to the object being viewed is called the line of sight.
Q 4
The angle of elevation is formed when an observer looks downward at an object from a higher point.
Q 5
The angle between the horizontal line through the eye and the line of sight when looking up is called the angle of elevation.
Q 6
The angle of depression is measured from the vertical line down to the line of sight.
Q 7
In height and distance problems of this chapter, all triangles considered are right-angled triangles.
Q 8
The height of an object can be found using trigonometric ratios without knowing any horizontal distance.
Q 9
In this chapter, problems may involve both angle of elevation and angle of depression in the same figure.
Q 10
The angle of elevation of the top of a tower from a point on the ground decreases as the observer moves closer to the tower.
Q 11
When the height of an object is fixed, the longer its shadow on level ground, the smaller the Sun’s altitude (angle of elevation).
Q 12
The line of sight is always horizontal.
Q 13
The distance between two points on a horizontal plane is taken as the base of the right triangle in height and distance problems.
Q 14
The height of a kite above the ground can be found using the length of its string and the angle it makes with the horizontal, assuming no slack.
Q 15
To solve numerical problems in this chapter, it is not necessary to draw a rough figure.
Q 16
If the angle of elevation of the top of a building is \(45^\circ\) and the distance from the observer to the building is known, the height of the building equals that distance.
Q 17
In this chapter, the trigonometric ratios \(\sin \theta,\ \cos \theta, \text{ and }\tan \theta\) are used, but \(\cot \theta,\ \sec \theta, \text{ and } \text{ cosec }\theta\) are never used.
Q 18
The term “height” in this chapter always refers only to the height of buildings.
Q 19
In angle of depression problems, the observer is usually at a higher level than the object being observed.
Q 20
In all examples of this chapter, the ground is assumed to be horizontal and level unless stated otherwise.
Q 21
When the angle of elevation increases but the height of the object remains the same, the observer must be moving away from the object.
Q 22
The distance of a ship from a lighthouse can be found by using the height of the lighthouse and the angle of elevation of its top from the ship.
Q 23
The angle of elevation of the top of a tower from a point on the ground is always greater than \(90^\circ\).
Q 24
While solving questions of this chapter, it is often useful to convert word problems into algebraic equations involving trigonometric ratios.
Q 25
The chapter “Some Applications of Trigonometry” introduces new trigonometric identities that are not used in previous chapters.
Key Takeaways — SOME APPLICATIONS OF TRIGONOMETRY
Core facts for CBSE Boards & exams
1
Angle of elevation is measured UPWARD from horizontal; angle of depression DOWNWARD.
2
tanθ = height/distance — the primary formula for heights and distances.
3
When the angle of elevation increases, the observer moves CLOSER to the object.
4
Angle of elevation from A to B = Angle of depression from B to A (alternate angles).
5
Height = distance × tan(angle of elevation).
6
For two observation points, set up two equations using tan for each angle.