Question

Esi is riding vertically in a hot air balloon, directly over a point, P on the ground. Esi spots a packed car on the ground at an angle of depression of 30 degrees. the balloon rises 50 metres. Now the angle of depression to the car is 35 degrees. How far is the car from point P

Answer 1

Correct Question :- Esi is riding vertically in a hot air balloon, directly over a point, P on the ground. Esi spots a packed car on the ground at an angle of depression of 30 degrees. the balloon rises 50 metres. Now the angle of depression to the car is 45 degrees. How far is the car from point P ?

Solution :-

from image we have,

• AP = Let x m.
• AC = 50 m.
• car is at Point B .
• ∠ABP = 30°
• ∠CBP = 45° .

In right ∆APB, we have,

→ tan 30° = AP / PB

→ (1/√3) = x / PB

→ PB = √3x m .

In right ∆CPB ,

→ tan 45° = CP / PB

→ 1 = (50 + x) / PB

→ PB = (50 + x) m.

therefore,

→ √3x = 50 + x

→ √3x - x = 50

→ x(√3 - 1) = 50

→ x = 50/(√3 - 1)

→ x = 50(√3 + 1)/(3 - 1)

→ x = 25(√3 + 1) m .

hence,

→ PB = √3 * 25 * (√3 + 1)

→ PB = 25(3 + √3) m (Ans.)

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