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

Name: 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
Uploaded: Mon, 2021-02-01 19:27
Description: 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

#Exemplar Maths for Class 10
#Introduction to Trigonometry
#Maths
#NCERT

#1.3
#8.2
#8.3
#8.4
#8.1
#9.2

1.0
1.0
1.0
1.0
2.0
2.0
2.0
2.0
2.0
2.0
3.0
3.0
3.0
3.0
4.0
4.0
4.0
4.0
5.0
5.0
5.0
5.0
6.0
6.0
6.0
6.0
7.0
7.0
7.0
7.0
8.0
8.0
8.0
8.0
9.0
9.0
9.0
9.0
10.0
10.0
10.0
10.0
11.0
11.0
11.0
11.0
12.0
12.0
12.0
12.0
13.0
13.0
13.0
14.0
14.0
14.0
15.0
15.0
15.0
16.0
17.0
18.0

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.

Answers (1)

Solution

Let y be the height of the balloon from the second window
In $\bigtriangleup$ AOB
$\tan 30= \frac{y}{d} \; \; \left ( \because \tan \theta = \frac{Perpendicular}{Base} \right )$
$d= y\sqrt{3}\; \cdots \left ( 1 \right )$ $\left ( \because \tan 30= 1\sqrt{3} \right )$
In $\bigtriangleup$ OCD
$\tan 60= \frac{4+y}{d}$
$\sqrt{3}d= 4+y$
$d= \frac{4+y}{\sqrt{3}}\cdots \left ( 2 \right )$
Equating equation (1) & (2) we get
$y\sqrt{3}= \frac{4+y}{\sqrt{3}}$
$y\sqrt{3}\times \sqrt{3}= 4+y$
$3y-y= 4$
$2y= 4$
$y= \frac{4}{2}$
y = 2
Height of balloon = 2 + 4 + y
= 2 + 4 + 2
= 8m