Question

basin was sailing balloons in a street aadi wants to sail a big balloon he saw that a round balloon of radius i m subtends an angle of 60 degreees at his eye while the angle of elevation of its centre is 30 degrees find the height of the centre of the balloons

Answer 1

The height of the center of the balloon is 0.5 m.

Step-by-step explanation:

See the attached figure.

Let the center of the balloon is at C and the top of the balloon is at D.

If the point of observation is B, then from Δ ABD,

$\tan 60^{\circ} = \frac{AD}{AB} = \frac{x + 1}{d}$

⇒ d = 0.577(x + 1) .......... (1)

Again, from Δ ABC, we can write

$\tan 30^{\circ} = \frac{AC}{AB} = \frac{x}{d}$

⇒ d = 1.732x ........... (2)

Now, from equations (1) and (2) we have,

0.577x + 0.577 = 1.732x

⇒ 1.155x = 0.577

⇒ x = 0.5 m

Therefore, the height of the center of the balloon is 0.5 m. (Answer)