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

Respuesta :

Answer:

6.06 km

Step-by-step 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 = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos [tex]8^{o}[/tex]  = [tex]\frac{6}{x}[/tex]

0.9903 = [tex]\frac{6}{x}[/tex]

⇒ x = [tex]\frac{6}{0.9903}[/tex]

      = 6.0588

x = 6.06 km

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