A ladder leans against the side of a house. The angle of elevation of the ladder is $63^{\circ}$ when the bottom of the ladder is $16 \mathrm{ft}$ from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

Step 1 ：A ladder leans against the side of a house. The angle of elevation of the ladder is $63^{\circ}$ when the bottom of the ladder is $16 \mathrm{ft}$ from the side of the house. We need to find the length of the ladder.

Step 2 ：The ladder, the ground, and the wall of the house form a right triangle. The angle of elevation of the ladder is the angle between the ground and the ladder. The distance from the bottom of the ladder to the house is the adjacent side of the triangle. We need to find the length of the ladder, which is the hypotenuse of the triangle.

Step 3 ：We can use the cosine of the angle to find the length of the ladder. The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse. Therefore, we can set up the equation $\cos(63^{\circ}) = \frac{16 \mathrm{ft}}{\text{length of the ladder}}$.

Step 4 ：Solving this equation for the length of the ladder gives us $\text{length of the ladder} = \frac{16 \mathrm{ft}}{\cos(63^{\circ})}$.

Step 5 ：Calculating the above expression gives us the length of the ladder to be approximately 35.2 feet.

Step 6 ：Final Answer: The length of the ladder is approximately \(\boxed{35.2}\) feet.