At a given moment, a plane passes directly above a radar station at an altitude of 6 km. let θ be the angle that the line through the radar station and the plane makes with the horizontal. how fast is θ changing 12 min after the plane passes over the radar station? /h.

- 187.237 km/hr fast is θ changing 12 min after the plane passes over the radar station

Explanation:

Let the distance x and angle θ be defined as in the figure below. Then

Now, differentiate with respect to t, we get

Now, calculate the travel distance from radar station to plane after 12min

Distance,  

Substituting ‘x’ value, we get

Find the rate of change of theta after 12 min,

We know, the formula for,

So, then,

When express the value in km/he, we get, the change in theta as

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