The angles of depression of two ships from the top of a light house are 45° and 30° towards east. if the ships are 200 m apart, find the height of the light house .

100 m
173 m
200 m
273 m

Correct Answer: 273 m

Explanation:

Let us draw a figure below as per given question.
Let AB = h meter be the height of the tower and two ships are situated at D and C respectively; such that, CD = 200 m; ∠ADC = 30° ∠ACB = 45° and BC = x meter (say)
Now from right triangle ABC,
tan 45° = h/x ⇒ 1 = h/x
∴ x = h
Again from right triangle ABD,
tan 30° = h/( 200 + x )
⇒ 1/√3 = h/( 200 + x )
Since x = h , we will get.
⇒ 1/√3 = h/(200 + h )
⇒ (200 + h ) = h X √3
⇒ h X √3 - h = 200
⇒ h x 1.732 - h = 200
⇒ h(1.732 - 1) = 200
∴ h = 200/0.732 = 273.2 m = 273 m

← Previous Question Next Question→

More Questions from Height and Distance

At a point on a level plane a tower subtends an angle Θ and a flag-staff a ft. in length at the top of the tower subtends an angle Θ . The height of the tower is :
A 6 ft-tall man finds that the angle of elevation of the top of a 24 ft-high pillar and the angle of depression its base are complementary angles. Then the distance between pillar and man is?
Two ships leave a port at the same instant. One sails at 30km/hr in the direction N 32° E while the other sails at 20 km/hr in the direction S 58° E. After two hours the ships are distant from each other by.
ABC is a triangular park with AB = AC = 100 meters. A clock tower is situated at the mid-point of BC. The angles of elevation of the top of the tower of A and B are cot -1 (3.2) and cosec -1(2.6) respectively. The height of the tower in meters is?
ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is Θ then Tan Θ equal to?
The height of the center of the round balloon of radius r, which subtend an angle ∝ at the eye of an observer and the elevation of whose center from the eye is β, is given by?
At a point on a level plane a tower subtends an angle θ and a flag-staff a ft. in length at the top of the tower subtends an angle ɸ. The height of the tower is :
A tower stands on a horizontal plane. A man on the ground 100 m from the base of the tower finds the angle of elevation of the top of the tower to be 30°. What is the height of the tower?
The upper part of a tree broken by the wind makes an angle of 30° with the ground and the distance from the root to the point where the top of the tree touches the ground is 10 m. What was the height of the tree?
In a rectangle, if the angle between a diagonal and a side is 30° and the length of diagonal is 6 cm, the area of the rectangle is :

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion