Question

FOR 50 POINTS SAHI DO OR LE JAO
the angle of a plane from point a on the ground is 60 degree after a flight of 10 seconds the angle of elevation changes to 30 degree of the plane is flying at a speed of 900 km per hour. find the height of the plane.​

Answer 1

From Image we can say That :-

→ AB = Height of Plane .

→ CD = Distance Travelled by plane in 10 seconds.

→ Angle ACB = 60°

→ Angle ADC = 30° .

Now, in Rt∆ABC, we Have :-

→ Tan60° = (AB/BC)

→ √3 = h/BC

→ h = BC * √3 ---------------- Equation (1)

Now, in Rt∆ABD , we have :-

→ Tan30° = AB / BD

→ (1/√3) = h /BD

→ h = (BD/√3) ---------------- Equation (2).

Comparing Value of h , from Both Equations we get,

→ BC * √3 = (BD/√3)

→ 3BC = BD

Or,

→ 3BC = BC + CD

→ 3BC - BC = CD

→ CD = 2BC ----------------- Equation (3).

____________________

Now, Speed of Plane is = 900km/h , Or, = 900 * (5/18) = 250m/s.

→ Time Taken By Plane to Go From Point C to D = 10 seconds .

→ So, Distance CD = Speed * Time .

→ CD = 250 * 10 = 2500m. ----------- Equation (4).

Putting Value of Equation (4) in Equation (3) we get,

→ CD = 2BC

→ 2500 = 2BC

→ BC = 1250m.

Putting value of BC in Equation (1) now, we get,

→ h = 1250 * √3 = 1250√3m.

Hence, Height of Plane is 1250√3m.

Answer 2

${\boxed{\mathtt{\purple{Answer}}}}$

Height of the Plane from ground is 1250√3 m

${\boxed{\mathtt{\purple{Solution}}}}$

Given that :-

The angle of plane AB from point a = 60°

After 10 sec . Angle from point C = 30°

Speed of plane = 900km / hr

_________________________

Speed of plane = 900 km / hr

$\implies \: \frac{900 \times 1000}{60 \times 60}$

$\implies \: \frac{9000}{36}$

Speed = 250 m / sec

Now ,

$\implies \: \tan( \theta) = \frac{perpendicular}{base}$

$\implies \: \tan(30) \: = \: \frac{h}{2500 + x}$

$\implies \: \frac{1}{ \sqrt{3} } \: = \: \frac{h}{2500 + x }$

$\boxed{\implies \: h \: = \: \frac{2500 + x}{ \sqrt{ 3} } }$

From the other angle :-

$\tan(60) = \frac{h}{x}$

$\boxed{ \implies \: \sqrt{3} x \: = \: h}$

Equating both values of h

$\implies \: \frac{2500 + x}{ \sqrt{3} } \: = \: \sqrt{3} x$

$\implies \: 2500 + x \: = \: 3x$

$\implies \: 2500 = 2x$

$\implies \: x \: = \: \frac{2500}{2} = 1250$

Putting value of x

$\implies \:h \: = \: \sqrt{3} \times x = \sqrt{3} \times 1250$

$\boxed {h \: = \: 1250 \sqrt{3}m}$