3. A ladder leans against a house making a 30^ angle with the ground. If the ladder touches the house at a point 10 feet high, how long is the ladder?

Step 1 ：This problem involves a right triangle, where the angle between the ladder and the ground is given, and the height at which the ladder touches the house is also given. We are asked to find the length of the ladder, which is the hypotenuse of the triangle.

Step 2 ：We can use the sine of the angle, which is the ratio of the opposite side (height) to the hypotenuse (length of the ladder), to find the length of the ladder.

Step 3 ：Given: angle = 30 degrees, height = 10 feet

Step 4 ：Using the formula for sine, we have \(\sin(30) = \frac{height}{ladder\_length}\)

Step 5 ：Solving for ladder_length, we get \(ladder\_length = \frac{height}{\sin(30)}\)

Step 6 ：Substituting the given values, we get \(ladder\_length = \frac{10}{\sin(30)}\)

Step 7 ：The length of the ladder calculated is approximately 20 feet.

Step 8 ：Final Answer: The length of the ladder is \(\boxed{20}\) feet.