Question

A whale comes to the surface to breathe and then dives at an angle of 20.0 ∘ below the horizontal. If the whale continues in a straight line for 200 m , how deep is it?

Answer 1

It is 68.404 m deep.

Step-by-step explanation:

The motion of the whale can be seen in the form of a right-angle triangle.

Angle of deviation = 20°

We know that, sinФ = Perpendicular/ Hypotenuse.

Here, hypotenuse = 200 m

Depth is perpendicular that we have to find.

sin(20°) = Depth/200

Depth = sin(20°) * 200 = 68.404 meters.

Answer 2

The depth is 68.4 meters.

Step-by-step explanation:

In this question the whale rose to the surface of the ocean to breath and then dives into the ocean at an angle of 20° below the horizontal line. It then travels 200 m straight along this line. We have to determine the depth of the ocean.

The path of the whale forms the hypotenuse of a right triangle and the angle between the hypotenuse and base is given as 20°. Determination of sides or angles in a right triangle can be determines using trigonometry.

sinθ =
`((opposite \ side))/(hypotenuse)`

opposite side = sinθ
`* hypotenuse`

Here θ = 20°

sinθ = sin(20°) = 0.342

opposite side=
`0.342 * 200 = 68.4 m`

Hence the depth is 68.4 m.