Question

An airplane takes off at an angle of 75° from its starting point. when the plane has traveled a total distance of 600 feet, its vertical height above the runway to the nearest foot is _____.

Answer 1

Height, h = 580 ft

Step-by-step explanation:

It is given that,

The distance traveled by the plane, d = 600 feet

The airplane takes off at an angle of 75° from its starting point.

Let h is the vertical height above the runway. It is the trigonometric problem. Let h is the height of the vertical height above the runway. It can be calculated using the trigonometric formula as :

`sin\theta=(h)/(d)`

`sin(75)=(h)/(600)`

h = 579.55 feet

or

h = 580 ft

So, the vertical height above the runway is 580 feet. Hence, this is the required solution.

Answer 2

Draw a right triangle so that its hypotenuse is 600 ft. The adjacent side is below the vertical, and it makes an angle of 75° with the hypotenuse.

Let h = height of the right triangle.
By definition,
sin75° = h/600
h = 600*sin75° = 579.555 = 580 ft (nearest ft)

Answer: 580 ft (nearest foot)