A ladder is leaned 9m up a wall with its base 5m from the wall. What angle does the ladder make with the ground?

Hint:

cos(θ)=adjacent/hypothenuse (CAH)

To find the angle that the ladder makes with the ground, we can use trigonometry. In this case, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the opposite side is the height of the ladder against the wall (9m), and the adjacent side is the distance from the base to the wall (5m).

So, we have tan(angle) = opposite/adjacent.
Substituting the values we have: tan(angle) = 9/5.

To find the angle, we can take the arctan (inverse tangent) of both sides, which gives us:
angle = arctan(9/5).

Using a calculator or a math tool, we can calculate arctan(9/5) to find the angle. In this case, the angle is approximately 59.04 degrees.

Therefore, the ladder makes an angle of approximately 59.04 degrees with the ground.