Question

Window45°Apartment450BenchNoah can see a bench in the nearby play area through his window inhis apartment at a 45° angle of depression.If the floor of the apartment that Noah is standing is 25 feet abovethe ground level, what is the horizontal distance from the apartmentto the bench in the play area?

Answer 1

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,

`\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \theta=(h)/(x) \end{gathered}`

Substitute the values and solve the equation for x.

`\begin{gathered} \tan 45^(\circ)=\frac{25\text{ ft}}{x} \\ 1=\frac{25\text{ ft}}{x} \\ x=25\text{ ft} \end{gathered}`

Therefore, the horizontal distance from the apartment to the bench is 25 ft.