Question

Basin was sailing the balloons in a street. Aadi wants to sail a big balloon. He saw that a round
balloon of radius im subtends an angle 60°
at his eye while the angle of elevation of its
centre is 30°. Find the height of the centre of
the balloons.​

Answer 1

Answer:√2

Step-by-step explanation:

Answer 2

Answer:

The height of the center of the balloon is  r  unit .

Step-by-step explanation:

Given as :

P is the eye of the observer

Let PA and PB be the tangent on balloon with center O

Let PX is the horizontal and CQ ⊥ PQ

∠CPA = ∠CPB = $\frac{60^{\circ}}{2}$

Or, ∠CPA = ∠CPB = 30°

And , ∠CPX = 60°

Let The height of the center of the balloon = h

CA = CB = r

In Δ CPB

Sin 30°  = $\dfrac{BC}{CP}$

Or, 0.5 = $\dfrac{r}{CP}$

Or, CP = $\dfrac{r}{0.5}$                ......1

Again

In Δ CPQ

Sin 30° = $\dfrac{CQ}{CP}$

Or, 0.5 = $\dfrac{h}{CP}$

Or, h = 0.5 × CP

Or, h = 0.5 × $\dfrac{r}{0.5}$  ( from eq 1)

∴    h =  r

i,e h = r  unit

So, The height of the center of the balloon = h =  r  unit

Hence, The height of the center of the balloon is  r  unit . Answer