Question

24. An airplane is approaching point A along a straight line and at a constant altitude h
At 10:00 am, the angle of elevation of the airplane is 20° and at 10:01 am, it is 60degree

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i What is the distance 'd' is covered by airplane from 10:00 am to 10:01 am if the
speed of the airplane is constant and equal to 600 miles/hour?
ii. What is the altitude 'h' of the airplane? (round answer to 2 decimal places).​

Answer 1

d = 10 miles

h = 4.61 miles.

Step-by-step explanation:

See the diagram attached.

Let at 10 : 00 a.m. the position of the plane was C and at 10 : 01 a.m. the position is D.

Now, point A is the observation point.

Now, from Δ ABC, $\tan 20^{\circ} = \frac{BC}{AB} = \frac{h}{x + d}$

⇒ $x + d = \frac{h}{\tan 20^{\circ}} = 2.75h$ ............. (1)

Again, from Δ  AED, $\tan 60^{\circ} = \frac{DE}{AE} = \frac{h}{x}$

⇒ x = 0.58h ............... (2)

Now, from equations (1) and (2) we get,

(x + d) - x = (2.75 - 0.58)h

⇒ d = 2.17 h ............ (3)

Now, the plane is moving at the speed of 600 mph.

So, in one minute it will travel by $\frac{600}{60} = 10$ miles.

Therefore, d = 10 miles. (Answer)

And from equation (3) we get,

10 = 2.17 h

⇒ h = 4.61 miles (Approx.) (Answer)

Answer 2

What is the distance 'd' is covered by airplane from 10:00 am to 10:01 am if the

speed of the airplane is constant and equal to 600 miles/hour?