Solved Examples of Angle of Depression

Problem 1: Find the angle of depression given the base and perpendicular of the 4 cm and 5 cm respectively.

Solution:

Angle of depression θ = tan^-1(p/b)

⇒ θ = tan^-1(5/4)

⇒ θ = 51.34°

Problem 2: Find the angle of depression given the base and hypotenuse of the 5 cm and 13 cm respectively.

Solution:

Angle of depression θ = cos^-1(b/h)

⇒ θ = cos^-1(5/13)

⇒ θ = 67.38°

Problem 3: Given the angle of depression formed when the observer is observing the object from top of a pole is 30°. The distance of the object from the pole is 100 m. Find the height of the pole.

Solution:

Angle of depression = 30°

Distance of the object from the pole = 100 m

⇒ tan θ = height / distance

⇒ tan 30° = h / 100

⇒ 0.577 = h / 100

Thus, Height of the tower h = 57.7 m

Problem 4: Given the height of the tower is 30 m and the distance of the object from the tower is 10 m. Find the angle of depression when the observer is in the tower and observing the object.

Solution:

Height of the tower = 30 m

Distance of the object from the tower = 10 m

Angle of depression θ = tan^-1(p/b)

⇒ θ = tan^-1(30 / 10)

⇒ θ = tan^-1(3)

⇒ θ = 71.56°

Problem 5: A mountaineer is watching camp from the top of a hill with an angle of depression of 30°. The height of the hill is 20km then find the length of the line of sight of the mountaineer.

Solution:

Length of line of sight = hypotenuse of the triangle

Angle of depression θ = 30°

Height of hill = 20km

⇒ sin θ = height of hill / length of line of sight

⇒ sin 30° = 20 / length of line of sight

⇒ Length of line of sight = 20 / sin 30°

⇒ Length of line of sight = 20 / (1/2)

⇒ Length of line of sight = 20 × 2

⇒ Length of line of sight = 40 km

Problem 6: The angle of depression of two ships from a lighthouse are 30° and 60° respectively. Given the height of the lighthouse is 5000 m and ship1 is 4000 m apart from the lighthouse. Find the distance between ship 1 and ship 2.

Solution:

We have drawn below figure according to the question

From the bigger triangle

tan 30° = 5000 / y

⇒ y = 5000 / tan 30°

⇒ y = 8660.25 m

From the smaller triangle

tan 60° = 5000 / z

⇒ z = 5000 / tan 60°

⇒ z = 2886.75 m

Since, from above figure y = x + z

x = y – z

⇒ x = 8660.25 – 2886.75

⇒ x = 5773.5 m

The distance between two ships (x) = 5773.5 m

Class 10 Resources on Angle of Depression:

• Applications of Trigonometry Class 10 Notes
• Applications of Trigonometry NCERT Solutions Class 10

Angle of Depression is one of the two important angles in Trigonometry, the other being the angle of elevation. The angle of depression refers to the angle at which one must look downward from a horizontal position to view an object situated at a lower level. It’s defined by the direct line from the observer to the object being observed, indicating a downward inclination of the line of sight.

In this article, we will learn about the Angle of Depression including various examples of the angle of depression and key differences between the angle of elevation and the angle of depression. We will also learn, how to calculate the angle of depression.