You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Horizontal Level and Line of Sight

A tree standi...

Question

A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively α and β. Prove that the height of the top from the ground is

$\frac{(b - a) \tan α \tan β}{\tan α - \tan β}$ .

Open in App

Solution

Let OP be the tree and A, B be the two points such OA = a and OB = b and angle of elevation to the tops are α and β respectively. Let OL = x and PL = h

We have to prove the following

The corresponding figure is as follows

In

…… (1)

Again in

…… (2)

Subtracting equation (1) from (2) we get

Hence height of the top from ground is .

Suggest Corrections

Similar questions

Q. Question 8
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height "h" units. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are

α

and

β

respectively. Prove that the height of the tower is

(\frac{h t a n α}{t a n β - t a n α})

A

pole is slightly inclined towards the east.

A

t two points due west of it at distances a and

b

, the angles of elevation of the top of the pole are

α

and

β

respectively. The inclination of the pole to the horizon is

Q. A chimney leans towards the north. At the points, equal distances due north and south of it in a horizontal plane, the elevations of the tops are

α

and

β

respectively. The inclination of the top of the chimney to the vertical is

Q. Two stations due South of a leaning tower which leans towards the North, are at distances

a

and

b

from its foot. If

α

and

β

are the elevations of the top of the tower from these stations, then prove that its inclination

θ

to the horizontal is given by

cot θ = \frac{b cot α - a cot β}{b - a}

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are $α$ and $β$ respectively. Find the height of the tower.

Join BYJU'S Learning Program

A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively α and β. Prove that the height of the top from the ground is (b-a)tan α tan βtan α -tan β.