Question

8. Angles of depression of two consecutive milestone on a straight road when observed
from an aeroplane vertically above the road are 45° and 30° respectively. If the
milestones are on the opposite sides of the aeroplane, then find the vertical height
of the aeroplane from the road.​

Answer 1

Answer:

(✓3+1)÷2 km

Explanation:

Let height of the aeroplane is h

Let two stones are at A and C and distance between two stones is 1 km.

Again from triangle AOB,

tan 45° = OB/OA

=> 1 = h/OA

=> OA = h

Now from triangle COB,

tan 35° = OB/OC

=> 1/√3 = h/(AC - OA)

=> 1/√3 = h/(1 - h)

=> 1/√3(1 - h) = h

=> 1-h =✓3h

=> 1= ✓3h-1h

=> (√3- 1)h = 1

=> h = 1/(√3 -1)

=> h = (✓3+1)÷(✓3-1) (✓3+1)

=> h = (✓3+1)÷(3-1)

=> h = (✓3+1)÷2 km

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