Example #1

Example:
You want to build stairs to the fourth story in an apartment building. The distance from the floor and the top of the stairs on each floor is 13 feet. You decide you want to makes the stairs at a 45 degree angle. You need to know how long to make the railing for all four stories. Assume that you need railings on only one side of the stairs, and that you don’t need railing on the “ends” of the stairs.  The amount of railing is equal to the “bottom” of the stairs.

Step 1: Since we know one angle measure, and it’s opposite leg, we can use the trigonometric function of sine (opposite/hypotenuse) to find the “hypotenuse”:

Sin(45) = 13

                                                                        H

Step 2: Multiply by “h” on both sides:

(h)(sin45) = 13

Step 3:  Divide both sides by sin 45

h= 13

       sin45

Step 4: Multiply 13/sin45 by 4 (for the four flights of stairs):

 (4)13

(1)sin45

Step 5: Simplify :

      52___

                                                                Sin45       equals approximately  73.54

Step 6:  You can’t have 73.54 feet of railing, so you need 74 feet of railing for all four stories.