Question

Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?☺✌​

Answer 1

Answer:

According to question,

Ram and Shyam are 10km away from each other.

Let say that hot air balloon is height h above the ground where Ram and Shyam are standing and also lets assume that the ballon is directly above from that point on ground which is x km away from Ram and so (10-x) km away from Shyam.

Now using Trigonometry,

Also, 60° is the angle which it made on Ram side and 30° is the angle which it made on Shyam side.

Therefore, tan60° = x/h and tan30° = (10-x)/h

So we can also write it as,

h = x/tan60° (1)

h = (10-x)/tan30° (2)

Equating (1) and (2):

x/tan60° = (10-x)/tan30°

You know that tan60° = √3 and tan30° = 1/√3, applying them in above equation, we will get:

x/√3 = (10-x)/(1/√3)

-> x/√3 = √3*(10-x)

Multiply √3 on both sides,

(x*√3)/√3 = √3*√3*(10-x)

x = 3*(10-x)

x = 30 - 3*x

Adding 3*x on both sides,

x + 3*x = 3*x +30 - 3*x

4*x = 30

Dividing 4 on both sides,

4*x/4 = 30/4

x = 7.5 km

This implies the point directly above which balloon is there is 7.5km away from Ram and 2.5km away from Shyam( Combining 7.5 + 2.5 = 10km).

Put value of x in either equation (1) or (2) to get the value of h (I'm putting it in (2), you can even put it in (1), the result will remain same in both cases)

h = (10 - 7.5)/(1/√3)

h = 2.5/(1/√3)

h = √3*2.5

So the height at which ballon is there is √3*(5/2) km or

4.33km (above the ground).

I hope you have understood the answer

Step-by-step explanation:

good evening

Answer 2

Step-by-step explanation:

actually answer accept noi ho Raha tha issliye screenshot hi sahi..bye