A 5.5 ft person is standing outside with an 8 foot long shadow. The shadow of a nearby street sign measured 12 ft long. How tall is the sign? I need help quickly

Answer 1

Because all the angles in your scenario are equal, the triangles created are similar. This, in turn, means that the side length are proportional.

The smaller triangle (with the person) has side lengths 5.5 and 8, the larger figure has a long leg of 12 ft. Your proportion, therefore, looks like this:

5.5/8 = x/12

Proportions are typically solved by cross multiplication (cross products). This would give you the following new equation: 5.5 x 12 = 8x

Simplify and divide both sides by 8 to get your answer.

Answer 2

This problem can be set up and solved as a proportion.

height of person = height of sign

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length of shadow length of shadow

5.5 = x

---- ---

8 12

You can solve this by cross multiplying.

(8)(x) = (5.5)(12)

8x = 66

--- ----

8 8

x = 8.25 ft is the height of the stop sign