SOME APPLICATIONS OF TRIGONOMETRY - True/False

The chapter “Some Applications of Trigonometry” mainly deals with problems on heights and distances.

In this chapter, angles are always measured in radians.

The line joining the observer’s eye to the object being viewed is called the line of sight.

The angle of elevation is formed when an observer looks downward at an object from a higher point.

The angle between the horizontal line through the eye and the line of sight when looking up is called the angle of elevation.

The angle of depression is measured from the vertical line down to the line of sight.

In height and distance problems of this chapter, all triangles considered are right-angled triangles.

The height of an object can be found using trigonometric ratios without knowing any horizontal distance.

In this chapter, problems may involve both angle of elevation and angle of depression in the same figure.

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.

When the height of an object is fixed, the longer its shadow on level ground, the smaller the Sun’s altitude (angle of elevation).

The line of sight is always horizontal.

The distance between two points on a horizontal plane is taken as the base of the right triangle in height and distance problems.

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.

To solve numerical problems in this chapter, it is not necessary to draw a rough figure.

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.

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.

The term “height” in this chapter always refers only to the height of buildings.

In angle of depression problems, the observer is usually at a higher level than the object being observed.

In all examples of this chapter, the ground is assumed to be horizontal and level unless stated otherwise.

When the angle of elevation increases but the height of the object remains the same, the observer must be moving away from the object.

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.

The angle of elevation of the top of a tower from a point on the ground is always greater than \(90^\circ\).

While solving questions of this chapter, it is often useful to convert word problems into algebraic equations involving trigonometric ratios.

The chapter “Some Applications of Trigonometry” introduces new trigonometric identities that are not used in previous chapters.