We can solve this problem using trigonometry. In this scenario, we have a right triangle formed by the ladder, the wall, and the ground.

• The length of the ladder (hypotenuse) is 16 feet.
• The height that the ladder reaches on the wall (opposite side) is 14.9 feet.
• We need to find the angle the ladder forms with the wall (which is the angle between the ladder and the wall).

We can use the sine function for this:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Substitute the known values:

$\sin(\theta) = \frac{14.9}{16}$

Now, calculate:

$\sin(\theta) \approx 0.93125$

To find the angle $\theta$, take the inverse sine (also called arcsine) of 0.93125:

$\theta = \sin^{-1}(0.93125)$

Using a calculator:

$\theta \approx 68.9^\circ$

So, the angle the ladder forms with the wall is approximately 68.9 degrees.

Would you like more details or have any other questions?

Related questions:

1. How can you calculate the distance between the base of the ladder and the wall?
2. How would the angle change if the ladder were shorter or taller?
3. What other trigonometric functions could be useful to solve this problem?
4. If the ladder were to slide down the wall, how would this affect the angle?
5. How can we find the length of the ladder if we know the height and angle?

Tip: When dealing with right triangles, it's helpful to remember the basic trigonometric ratios: sine, cosine, and tangent.