Answer:
[tex]37.97 ^\circ[/tex]
Step-by-step explanation:
As shown in the attached figure, let AB be the slide of the playground which is actually hypotenuse of the [tex]\triangle ABC[/tex].
And vertical height be AC.
As per the question statement:
[tex]AB = 6.5 m\text{ and}\\AC = 4 m[/tex]
We have to find out the angle of depression [tex]\angle DAB[/tex] i.e. [tex]\theta[/tex] as shown in the figure attached.
By rule of alternate angles:
The angle of depression [tex]\angle DAB = \angle ABC[/tex].
[tex]\text{In } \triangle ABC:[/tex]
[tex]\\sin\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow sin\theta = \dfrac{AC}{AB}\\\Rightarrow sin\theta = \dfrac{4}{6.5}\\\Rightarrow sin\theta = 0.6153\\\Rightarrow \theta = 37.97 ^\circ[/tex]
So, angle of depression is [tex]37.97 ^\circ[/tex].
