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Calculate Height Using Proportions

Geometry and Proportions

If I am 5.5 and cast an 8 ft shadow, how do I figure out how tall a person is that casts a 9 ft shadow?

I know the answer is 74 inches but how do I work out the problem?

Comments for Calculate Height Using Proportions

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Feb 15, 2013
by: Staff


A geometric diagram of the two shadows and the height of the two people is shown below.

Length of Shadows - Similar Triangles

The two triangles are similar triangles. In this case, both triangles are also right triangles.

Each triangle has exactly the same shape as the other triangle.

The only difference is size. One triangle is larger than the other.

The three angles of each triangle are equal to the corresponding angle in the other triangle.

90° = 90°

∠A = ∠C

∠B = ∠D

When triangles are similar triangles, the ratio of corresponding sides is the same.

This allows you to set up a proportion to solve for the height of the person who casts the 9 foot shadow.

(h) is to (5 ft 5 in) as (9 foot shadow) is to (8 foot shadow)

(h) : (5 ft 5 in) as (9 foot shadow) : (8 foot shadow)

(h) : (5 ft 5 in) = (9 foot shadow) : (8 foot shadow)

(h) / (5 ft 5 in) = (9 foot shadow) / (8 foot shadow)

(h) / (65 in) = (108 in) / (96 in)

Now it's just a matter of solving for h.

Length of Shadows - Proportions

Final Answer:

h = 73.125 inches

Thanks for writing.


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