The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30° , respectively. Find the height of the balloon above the ground
Solution:
Given, the lower window of a house is at a height of 2 m above the ground
The upper window is 4 m vertically above the lower window.
The angles of elevation of a balloon from these windows are observed to be 60° and 30°
We have to find the height of the balloon above the ground.
From the figure,
W₁ be the upper window
W₂ be the lower window
Distance of the lower window from the ground, OR = 2m
Distance of the upper window from the top of the lower window, RQ = 4m
Angle of elevation of balloon from lower window, ∠BW₂R = 60°
Angle of elevation of balloon from upper window, ∠BW₁R = 30°
Height of the balloon from the ground, BO = h m
Distance between the point of observation to the foot, PO = xm
In triangle BW₂R,
tan60° = BR/W₂R
Since, tan60° = √3
√3 = BO - RO/PO
√3 = h - 2/x
x = h - 2/√3 ----------------(1)
In triangle BW₁R,
tan30° = BQ/W₁R
Since, tan30° = 1/√3
1/√3 = h - 6/x
Since,W₁R = PO = x
x = √3(h - 6)------------------------(2)
By comparing (1) and (2), we get,
h - 2/√3 = √3(h - 6)
h - 2 = 3(h - 6)
h - 2 = 3h - 18
3h - h = 18 - 2
2h = 16
h = 8m.
Therefore, the height of the balloon above the ground is 8m.
✦ Try This: A house of height 100 m substends a right angle at the window of an opposite house. If the height of the window is 64 m, then the distance between the two houses is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.4 Problem 18
The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30° , respectively. Find the height of the balloon above the ground
Summary:
The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At a certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30° , respectively. The height of the balloon above the ground is 8m
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