How high is the keyboard?

Question

You are making a wedge shaped piece of foam to place under the computer keyboard. The keyboard is five inches wide and 12 inches long. The angle of incline of the wedge, T, shown below, should have cos (T) = 5/7. The keyboard sits on top of the wedge so that there is an inch margin of the wedge showing on all sides. Find the height of the wedge to the nearest hundredth of an inch.

Answer 1

cos(T)=5/7. The slope length of the wedge is 2" longer than the width of the keyboard, i.e., 7". The base of the wedge must therefore be 5" long and by Pythagoras the height of the wedge is sqrt(7^2-5^2)=sqrt(24)=2sqrt(6)=4.90" to the nearest 1/100".