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An airplane pilot sights a life raft at a 26° angle of depression. The airplane's altitude
is 3 km. What is the airplane's surface distance d from the raft? Round your answer
to the nearest whole number.
A 5 Km
B 6 Km
C 4 km
D 3 Km

Respuesta :

mysticchacha

Answer:

Choice B.  6 km.

Step-by-step explanation:

We see this is a right triangle.

The height of this right triangle is 3 km and the angle adjacent to the height leg of the triangle is  (90 - 26 ) degrees = 64 degrees.

We want the distance d which is the leg opposite  64 degrees.

tan 64 = d / 3 km  ;

d = 3 * tan 64 =  3 * 2.0503038  km  = 6.1509 km

The airplane's surface distance from the raft is 6 Km.

What is a right angle triangle?

'A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.'

According to the given problem,

The airplane's altitude = 3 km

Let the surface distance of the airplane from the raft be d,

Assuming a right angle triangle,

Perpendicular = 3 km

Base = d

θ = 26°

We know, tanθ = [tex]\frac{Perpendicular}{Base}[/tex]

            ⇒ tan26 = [tex]\frac{3}{d}[/tex]

            ⇒ d = [tex]\frac{3}{tan26}[/tex]

            ⇒ d = 6.15 km

            ⇒ d ≈ 6 km

Hence, we can conclude, the airplane's surface distance from the raft is 6 km.

Learn more about right angle triangle here: https://brainly.com/question/3770177

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