Question

a plane is flying horizontally at a height of 10000m above a level stretch of ground at a constant speed of 240 km/h. A man on the ground observes the angle of elevation of the plane (which is flying on a course directly towards him) to be 35 degrees. how far (to the nearest km) in a straight line is the man from the plane, 1 minute after he measured the angle of elevation?

Answer 1

let the horizontal distance, along the ground, be x km
so 10 km/x km = tanØ
when Ø = 35°, 10/x = tan35
x = 14.2815 km
that distance x is decreasing at 240km/h
= 240km/60 m = 4 km/min
so 1 minute later, x = 14.2815 - 4 = 10.2815 km

hypotenuse distance^2 = 10^2 + 10.2815^2
hypotenuse distance = 14.343 km or 14 km to the nearest km