Height and Distance · Mathematics · NDA

Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15$$^\circ$$ with the horizontal. The distance between the poles is approximately equal to

A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30$$^\circ$$ and 45$$^\circ$$, respectively. Which one of the following gives the best approximation to the height of the tower?

The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill?

A moving boat is observed from the top of a cliff of 150 m height. The angle of depression of the boat changes from 60$$^\circ$$ to 45$$^\circ$$ in 2 minutes. What is the speed to the boat in metres per hour?

The angle of elevation of a stationary cloud from a point 25m above a lake is 15$$^\circ$$ and the angle of depression of its image in the lake is 45$$^\circ$$. The height of the cloud above the lake level is

The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30$$^\circ$$ and 45$$^\circ$$. If h_T is the height of the tower and h_P is the height of the pole, then which of the following are correct?

1. $${{2{h_P}{h_T}} \over {3 + \sqrt 3 }} = h_P^2$$

2. $${{{h_T} - {h_P}} \over {\sqrt 3 + 1}} = {{{h_P}} \over 2}$$

3. $${{2({h_P} + {h_T})} \over {{h_P}}} = 4 + \sqrt 3 $$

Select the correct answer using the code given below.

From the top of a lighthouse, 100 m high, the angle of depression of a boat is $${\tan ^{ - 1}}\left( {{5 \over {12}}} \right)$$. What is the distance between the boat and the lighthouse?

A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48$$^\circ$$. If the height of the balloon above the bridge is 122m, then what is the length of the bridge?

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation $${\pi \over 6}$$ and $${\pi \over 3}$$ respectively. What is the height of the hill?

If a flage-staff of 6m height placed on the top of a tower throws a shadow of $$2\sqrt 3 $$ m along the ground, then what is the angle that the sun makes with the ground?

A spherical balloon of radius r subtends an angle $$\alpha$$ at the eye of an observer, while the angle of elevation of it centre is $$\beta$$. What is the height of the centre of the balloon (neglecting the height of the observer) ?

A ladder 9m long reaches a point 9m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60$$^\circ$$. What is the height of the flagstaff?

The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y. If AB = z, then which one of the following is correct?

If x is the distance of P from the bottom of the pillar, then consider the following statements :

1. x can take two values which are in the ratio 1 : 3

2. x can be equal to the height of the flagstaff

Which of the statements given above is/are correct? 

What is a possible value of tan θ ? 

What is the height of the lamp post ?

At what height is the top of the tower above the ground level ?

If θ is the inclination of the tower to the horizontal, then what is cot θ equal to ?

What is the length of the tower ?

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively. What is the height of the tower ?

The shadow of a tower becomes x metre longer, when the angle of elevation of sun changes from 60° to θ. If the height of the tower is $\sqrt{3}x$ metre, then which one of the following is correct ?

A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75°. What is the height of the Flagstaff?

The shadow of a tower is found to be x meter longer, when the angle of elevation of the sun changes from 60° to 45°. If the height of the tower is 5(3 + √3) m, then what is x equal to?