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An aeroplane is moving at a constant altitude 'h'. At 10:00 AM, it is seen at an elevation of 30°. 1 minute later, it is observed at an elevation of 60°. If the speed of the plane is 960 km/h, then find 'h'.

A13.86 km

B15 km

C12.46 km

D20 km

Answer:

A. 13.86 km

Read Explanation:

image.png

Distance traveled

=96060=16km=\frac{960}{60}=16 km

d1−d2=16kmd_1-d_2=16km

tan30=hd1⇒d1=htan30tan 30 = \frac{h}{d_1} \Rightarrow d_1=\frac{h}{tan30}

tan60=hd2⇒d2=htan60tan 60 = \frac{h}{d_2} \Rightarrow d_2=\frac{h}{tan60}.

=htan30−htan60=\frac{h}{tan30}-\frac{h}{tan60}

=h13−h3=16=\frac{h}{\frac{1}{\sqrt3}}-\frac{h}{\sqrt3}=16

=h=83=13.85km=h=8\sqrt3=13.85 km


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