A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67 5^ . What is the height of the plane above the ground ?

Step-by-step solution

Let h be the height of the plane above the ground. The distance from the point of observation to the plane is d = 10 km. The angle of elevation is = 67.5^ . From the right-angled triangle formed, = h d . h = 10 67.5^ Using the half-angle formula, = 1 - 2 2 . 67.5^ = 1 - 135^ 2 = 1 - (- 1 2 ) 2 = 2 + 1 2 2 Multiplying the numerator and denominator inside the square root by 2 : 67.5^ = 2 + 2 4 = 2 + 2 2 Substituting this value into the equation for h : h = 10 2 + 2 2 = 5 2 + 2 km