Indirect Measurement Math Example 3

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Example 3

easy
A 66-foot person casts a 44-foot shadow. At the same time, a nearby flagpole casts a 2020-foot shadow. How tall is the flagpole?

Solution

  1. 1
    Set up the proportion: 64=h20\frac{6}{4} = \frac{h}{20}.
  2. 2
    Solve: h=6×204=1204=30h = \frac{6 \times 20}{4} = \frac{120}{4} = 30 feet.

Answer

The flagpole is 3030 feet tall.
Shadow proportion problems use similar triangles. The ratio of height to shadow length is the same for all objects measured at the same time of day, because the sun's rays are effectively parallel.

About Indirect Measurement

Indirect measurement finds unknown lengths by using proportional relationships instead of direct measuring tools.

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More Indirect Measurement Examples

Example 1 medium

A tree casts a shadow of [formula] m at the same time a [formula] m pole casts a shadow of [formula]

Example 2 hard

From a point [formula] m from the base of a building, the angle of elevation to the top is [formula]

Example 4 medium

To measure river width, a surveyor marks [formula] and [formula] on one bank with [formula] m. A tre

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