Question

A particular airport has beacons on the ground 6 km out from the start of each runway. An airplane is directly over this beacon and is at an angle of elevation from the runway of 8°. Calculate the direct line distance from the airplane to the start of the runway

Answer 1

6.06 km

Explanation:

The information given in the question can be represented by the three sides if a right angled triangle.

Let the direct line from the airplane to the start of the runway be represented by x. So that applying the appropriate trigonometric function, we have;

Cos θ =
`(adjacent)/(hypotenuse)`

Cos
`8^(o)` =
`(6)/(x)`

0.9903 =
`(6)/(x)`

⇒ x =
`(6)/(0.9903)`

= 6.0588

x = 6.06 km

The direct line from the airplane to the stat of the runway is 6.06 km.