Student's math problem solving a real-world trigonometry question about shooting a basketball at the correct angle.

Let’s solve this step by step.

We’re told:
- The basketball goal is 40 ft tall → that’s the vertical side (opposite).
- Its shadow is 20 ft long → that’s the horizontal side (adjacent).
- We want to find the angle from the ground up to the top of the goal — that’s the angle we’d shoot at if we were standing at the end of the shadow and aiming for the top of the goal.

This forms a right triangle:
- Opposite = 40 ft
- Adjacent = 20 ft
- Angle x is between the adjacent side (ground) and the hypotenuse (line of sight/shoot path).

To find the angle when you know opposite and adjacent, use tangent:

> tan(x) = opposite / adjacent
> tan(x) = 40 / 20
> tan(x) = 2

Now, to find the angle whose tangent is 2, we use the inverse tangent function:

> x = tan⁻¹(2)

Using a calculator (make sure it’s in degree mode):

> tan⁻¹(2) ≈ 63.4349...°

Rounded to one decimal place: 63.4°

✔ Double-check:
If tan(x) = 2, then x should be more than 45° (since tan(45°)=1), and less than 90°. 63.4° makes sense.

Final Answer:
63.4°