Given:
The angle of depression of the bench with respect to Noah, θ=45° .
The height of the apartment or the height at which Noah is standing with respect to the ground, h=25 feet.
Let x be the horizontal distance from the apartment to the bench.
Now, using trigonometric property in the above triangle,
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \theta=\frac{h}{x} \end{gathered}[/tex]Substitute the values and solve the equation for x.
[tex]\begin{gathered} \tan 45^{\circ}=\frac{25\text{ ft}}{x} \\ 1=\frac{25\text{ ft}}{x} \\ x=25\text{ ft} \end{gathered}[/tex]Therefore, the horizontal distance from the apartment to the bench is 25 ft.
