Class 10 Maths Applications of Trigonometry Angle of Elevation & Depression

Angle of Elevation & Depression

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e., the case when we raise our head to look at the object.

The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e., the case when we lower our head to look at the point being viewed.

Numerical: The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

Solution:  let height of tower be x.

Tan 30o = AB/BC

Or   1/√3 = x/30

Or x = 10√3

Thus height of tower is 10√3 m.

Numerical: As observed from top of a 75 m high lighthouse from sea-level, angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on same side of lighthouse, find the distance between the two ships.

Solution: Let the distance between the ships be y.

In right Δ ABC,

Tan 45o =AB/BC

Or 1 = 75 m /x

Or x = 75 m

In right Δ ABD,

Tan 30o = AB /BD

Or  1/√3 = 75 m / (x + y)    = 75 m / (75 + y)

Or y = 75 (√3 -1) m

Thus distance between ships is 75 (√3 -1) m

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