Question

A playground slide is 6.5 meters long, and covers a vertical distance of 4.0 meters, as shown in the diagram.

To the nearest degree, what is the measure of θ, the angle of depression?

Answer 1

`37.97 ^\circ`

Explanation:

As shown in the attached figure, let AB be the slide of the playground which is actually hypotenuse of the
`\triangle ABC`.

And vertical height be AC.

As per the question statement:

`AB = 6.5 m\text{ and}\\AC = 4 m`

We have to find out the angle of depression
`\angle DAB` i.e.
`\theta` as shown in the figure attached.

By rule of alternate angles:

The angle of depression
`\angle DAB = \angle ABC`.

`\text{In } \triangle ABC:`

`\\sin\theta = (Perpendicular)/(Base)\\\Rightarrow sin\theta = (AC)/(AB)\\\Rightarrow sin\theta = (4)/(6.5)\\\Rightarrow sin\theta = 0.6153\\\Rightarrow \theta = 37.97 ^\circ`

So, angle of depression is
`37.97 ^\circ`.