7. an airplane takes off 200 yards in front of a 60 foot building. at what angle of elevation must the plane…

7. an airplane takes off 200 yards in front of a 60 foot building. at what angle of elevation must the plane take off in order to avoid crashing into the building? assume that the airplane flies in a straight line and the angle of elevation remains constant until the airplane flies over the building.

7. an airplane takes off 200 yards in front of a 60 foot building. at what angle of elevation must the plane take off in order to avoid crashing into the building? assume that the airplane flies in a straight line and the angle of elevation remains constant until the airplane flies over the building.

Answer

Explanation:

Step1: Convert yards to feet

Since (1) yard ( = 3) feet, (200) yards (=200\times3 = 600) feet.

Step2: Use the tangent function

The tangent of an angle of elevation (x) in a right - triangle is given by (\tan x=\frac{\text{opposite}}{\text{adjacent}}). Here, the opposite side is the height of the building ((h = 60) feet) and the adjacent side is the horizontal distance ((d=600) feet). So, (\tan x=\frac{60}{600}).

Step3: Calculate the angle

(\tan x = 0.1). Then (x=\arctan(0.1)). Using a calculator, (x\approx5.71^{\circ})

Answer:

The angle of elevation is approximately (5.71^{\circ})