Aramp leading into a building makes a 15o angle with the ground. the end of the ramp is 10 feet from the base of the building.

approximately how long is the ramp? round to the nearest tenth.

Draw a right triangle to model the problem.

The height of the building (opposite side) is the vertical height of the triangle.
The horizontal (adjacent side) at the lower end of the height is the ground.
The hypotenuse, of length = x, is the ramp.
The given angle between the horizontal (adjacent side) and the hypotenuse is 15°.

By definition,
cos(15°) = adjacent/hypotenuse = 10/x
x*cos(15°) = 10
x = 10/cos(15°) = 10.353

The length of the ramp is 10.4 ft (nearest tenth)