CPM 4.2.3

Mr. Gow needs to build a wheelchair access ramp for the school’s auditorium. The ramp must rise a total of 3 feet to get from the ground to the entrance of the building. In order to follow the state building code, the angle formed by the ramp and the ground cannot exceed 4.76 degrees. 

Mr. Gow has plans from the planning department that call for the ramp to start 25 feet away from the building.  Will this ramp meet the state building code?

Draw an appropriate diagram.  Add all the measurements you can.  What does Mr. Gow need to know?

To determine an angle measure from a trigonometric ratio, you need to “undo” it, just like you can undo addition with subtraction, multiplication with division, or squaring by taking the square root.  These examples are all pairs of inverse operations.

When you use a calculator to do this, you use inverse trigonometric functions that are usually labeled “ $\sin^{-1}$  ”, “  $\cos^{-1}$   ”, and “  $\tan^{-1}$   ”.  These are pronounced “inverse sine”, “inverse cosine”, and “inverse tangent”.  On many calculators, you may need to press the “inv” or “2nd” key first, then the “sin”, “cos”, or “tan” key. 

Verify that your calculator can compute an inverse trig value using the triangle at right. When you compute $\cos^{-1}\left(\frac{8}{16}\right)$ 

 
do you get  $60\degree$ ?

For the triangle at right, determine the measures of ∠A and ∠B. Once you have solved for the measure of the first acute angle (either ∠A or ∠B), what knowledge about the angles in triangles could help you solve for the second acute angle measure?