Problem 47 - Algebra and Trigonometry

Question

A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 23 -foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.

Step-by-Step Solution

Answer

The angle of elevation of the ramp, rounded to the nearest tenth of a degree, is approximately 15.1 degrees.

Step 1: Identifying the problem

We are given a right-angled triangle and asked to find the angle of elevation. The opposite side (height of the ramp) is 6 feet, and hypotenuse (the ramp itself) is 23 feet.

Step 2: Applying trigonometric function

We find the sine of the angle, which is given by: sin(angle) = opposite/hypotenuse = 6/23.

Step 3: Finding the angle

To get the angle of elevation, we take the inverse sine of the result from Step 2. So, angle = sin^-1 (6/23).

Step 4: Calculation

Using a calculator, we find that sin^-1 (6 / 23) is approximately 15.1 degrees.

Step 5: Rounding to the nearest tenth

Finally, we round the calculated angle to the nearest tenth, resulting in an angle of 15.1 degrees.