Question

There are two windows in a house. A window of the house is at a height of 1.5 m above the ground and the other window is 3 m vertically above the lower window. Ram and Shyam are sitting inside the two windows. At an instant, the angle of elevation of a balloon from these windows are observed as 45° and 30° respectively. Find the height of the balloon from the ground.​

Answer 1

Answer:

this is the answer

Step-by-step explanation:

Given, two windows are at 1.5 m & 4.5 m from ground respectively.

AG=1.5 m,AB=3 m

⇒GB=4.5 m

Let OX=h(height of balloon from ground)

∴QX=(h−4.5)

Two perpendicular are dropped from A to B respectively to P & Q.

In right triangle APX

tan45=

AP

PX

⇒

AP

(h−4.5+3)

=1

⇒AP=(h−1.5)

∴BQ=(h−1.5)

So, in right triangle, BQX

tan30=

BQ

QX

=

3

1

⇒

h−1.5)

(h−4.5)

=

3

1

⇒

3

h−

3

(4.5)=(h−1.5)

⇒(

3

−1)h=

3

(4.5)−1.5

⇒h=

3

−1

3

(15)(3)−1.5

=8.6 m.

Hope it helps you!