d) A $15 \mathrm{~m}$ pole is leaning against a wall. The foot of the pole is $10 \mathrm{~m}$ from the wall. Find the angle that the pole makes with the ground.

Step 1 ：We have a right triangle with the pole as the hypotenuse, the distance from the wall as one leg, and the height of the wall where the pole touches as the other leg.

Step 2 ：We are given the length of the pole (hypotenuse) as 15 m and the distance from the wall (one leg) as 10 m.

Step 3 ：We can use the cosine function to find the angle between the pole and the ground. Cosine is defined as the adjacent side divided by the hypotenuse.

Step 4 ：In this case, the adjacent side is the distance from the wall (10 m) and the hypotenuse is the length of the pole (15 m).

Step 5 ：So, we have \(\cos(\theta) = \frac{10}{15} = \frac{2}{3}\).

Step 6 ：To find the angle \(\theta\), we take the inverse cosine of \(\frac{2}{3}\).

Step 7 ：\(\theta = \cos^{-1}(\frac{2}{3})\)

Step 8 ：Thus, the angle that the pole makes with the ground is \(\boxed{\cos^{-1}(\frac{2}{3})}\) degrees.