Question

Solve it with a proper explanation !!

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Answer 1

Given :

• speed of aeroplane = 360 km/h

• Angle of elevation when it is at point A. ( refer attachment) = 45°

• Angle of elevation when it is at point B after 10 seconds( refer attachment) = 30°

To find :

• height at which the aircraft was flying.

Concept used :

• tan x = perpendicular / base

• distance = speed × time

• 1 km = 1000 m

• 1 hour = 3600 seconds

Solution :

speed is given as = 360 km/h

⟹ so first we will convert 360 km/h in m/s .

⟹ 360 km/h = ( 360 × 1000)/3600

⟹ 360 km/h = 100 m/s

⟹ time = 10 seconds

We know, distance = speed × time

⟹ distance = 100 × 10

⟹ distance = 1000 m

therefore length of AB or CD ( because AB= CD) in diagram ( attachment) is = 1000m

Now It is given that ,Angle of elevation when it is at point A = 45°, i.e. angle ALC = 45°

⟹ tan 45° = AC / LC

we know that tan45° = 1

⟹ 1 = AC / LC

⟹ LC = AC

AC = BD = LC

Now , LD = LC + CD

Now It is given that ,Angle of elevation when it is at point B after 10 seconds( refer attachment) = 30° ,i.e. angle BLD = 30°

⟹ tan 30° = BD/LD

⟹ tan 30° = BD/(LC+CD)

AC = BD = LC

⟹ tan 30° = BD/(LC+CD)

AB= CD = 1000m and tan 30° = 1/√3

⟹ 1/√3 = BD/(BD+1000)

let BD be x :-

⟹ 1/√3 = x/(x+1000)

now cross multiply :-

⟹ x+1000 = √3 x

√3 = 1.732 ( given in question)

⟹ x+1000 = 1.732x

⟹ 1000 = 1.732x - x

⟹ 1000 = 0.732x

⟹ (1000/ 0.732)= x

⟹ 1366.12 = x

Therefore x = BD = height = 1366.12 m

Answer :

height at which which the aircraft was flying = 1366.12 metres

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Learn more :-

• speed = distance / time

• time = distance /speed

• one hour = 60 minutes

• One minute = 1/60 hours

• one hour = 3600 seconds

• 1 km = 1000 m

• 1 m = 1/1000 m

• 1 m = 100 cm

• 1 cm = 1/100 m

Also :-

• Sin 30° = 1/2

• cos 30° = √3/2

• tan 30° = 1/√3

• Sin 45° = 1/√2

• cos 45° = 1/√2

• tan 45° = 1

• Sin 60° = √3/2

• cos 60° = 1/2

• tan 60° = √3

• Sin 90° = 1

• cos 90° = 0

• tan 90° = infinite

• cosec x = 1/ sin x

• sec x = 1/ cosx

• cot x = 1/tan x

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Answer 2

Answer:

Step-by-step explanation:

speed is given as = 360 km/h

⟹ so first we will convert 360 km/h in m/s .

⟹ 360 km/h = ( 360 × 1000)/3600

⟹ 360 km/h = 100 m/s

⟹ time = 10 seconds

We know, distance = speed × time

⟹ distance = 100 × 10

⟹ distance = 1000 m

therefore length of AB or CD ( because AB= CD) in diagram ( attachment) is = 1000m

Now It is given that ,Angle of elevation when it is at point A = 45°, i.e. angle ALC = 45°