Height of A building?

Question

To find the height of building, you observe that a yard stick held vertically on the ground cast a shadow of 42 1/2". At the same time, the building cast a shadow which is measured at 57' - 7 3/4". How tall is the building?

Answer 1

Similar triangles:

Let's put all the units in inches first, so 57 ft 7.75 inches is:
57 * 12 + 7.75 = 691.75 inches

36 inch yard stick casts a 42.5 inch shadow
x inches building casts a 691.75 inch shadow

36 / 42.5 = x / 691.75

Cross multiply:
42.5 x = 691.75 * 36
x = (691.75 * 36) / 42.5
x = 585.952941 inches

Dividing by 12, you get 48, with a remainder.
48 ft = 576 inches, remainder 9.952941 inches

So all together your building is 48 feet 9.95 inches, or approximately 48 ft. 10 inches.