Answer is below.
Let's call the height of the house "h".
The ladder is propped up against the house, forming a right triangle with the wall of the house and the ground. The ladder is the hypotenuse of the triangle, and the height of the house is one of the legs.
We know that the length of the ladder is 16 feet, and the angle of elevation is 62 degrees. We can use trigonometry to find the height of the house.
The trigonometric function that relates the angle of elevation to the height and length of the ladder is the tangent function:
tan(62) = h/16
To solve for h, we can multiply both sides by 16:
16 tan(62) = h
Using a calculator, we can evaluate the tangent of 62 degrees to get:
16 tan(62) ≈ 28.6
So the height of the house is approximately 28.6 feet.