91Ó°ÊÓ

The given condition includes the length of the wheelchair ramp (23 feet), and the final height of it (6 feet). These two measures form the hypotenuse and one side of a right triangle respectively. In order to find the angle of elevation, we have to apply the concept that in a right triangle, the tangent of the angle is the ratio of the side opposite to the angle to the side adjacent to the angle. In this case, the opposite side is the final height of the ramp, and the adjacent side is the horizontal distance from the base of the ramp to the library. However, this distance is unknown, so another approach by using sine could also be used since the sine of an angle in a right angled triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

The sine of the required angle can be calculated as the ratio of the final height of the ramp to the length of the ramp, i.e., \(\sin(\Theta) = \frac{6}{23}\).?

Here, \(\Theta\) is the required angle. We can find this by calculating the inverse sine (or arcsine) of the ratio. The angle of elevation, to the nearest tenth of a degree, can be calculated as \(\Theta = \arcsin \left(\frac{6}{23}\right)\). In most scientific calculators, this function is denoted as 'sin-1'.