The example on page 11 gives the height and shadow length of a totem pole and the height of a man. The shadow length of the man is unknown. Two different ratios are created and then set equal to each other in a proportion.
Ratio of man's height to totem pole's height
6 ft/90 ft
Ratio of man's shadow to totem pole's shadow
x ft/45 ft
Proportion
6 ft/90 ft = x ft/45 ft
Notice that each ratio compares a characteristic of the man to the corresponding characteristic of the totem pole. Instead, we can compare the man to himself, and the totem pole to itself. We will create one ratio for the man and one for the totem, comparing the shadow length and height of each one.
shadow length/height
We can then write a ratio for the man and a ratio for the totem pole.
Man:xft/6ft Totem Pole:45ft/90ft
Now we can write a proportion by setting the ratios equal to each other.
x/6 ft = 45 ft/90 ft
Solving the proportion for x will give us the length of the man's shadow. To isolate x, we will simplify the right-hand side and then multiply by 6 on both sides. Notice that all of the units are the same so we can remove them when performing the calculations.
