Indirect Measurement Math Example 1

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Example 1

medium
A tree casts a shadow of 1515 m at the same time a 22 m pole casts a shadow of 33 m. How tall is the tree?

Solution

  1. 1
    Set up a proportion using similar triangles: tree heighttree shadow=pole heightpole shadow\frac{\text{tree height}}{\text{tree shadow}} = \frac{\text{pole height}}{\text{pole shadow}}.
  2. 2
    Substitute known values: h15=23\frac{h}{15} = \frac{2}{3}.
  3. 3
    Cross-multiply: 3h=303h = 30, so h=10h = 10 m.

Answer

The tree is 1010 m tall.
When two objects cast shadows at the same time, the sun creates similar triangles. Corresponding sides of similar triangles are proportional, allowing the unknown height to be found from the known height-to-shadow ratio.

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 2 hard

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

Example 3 easy

A [formula]-foot person casts a [formula]-foot shadow. At the same time, a nearby flagpole casts a [

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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