Indirect Measurement - Using Similar Triangles

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Examples, solutions, videos, worksheets, stories, and songs to help Grade 8 students learn about indirect measurement (using similar triangles).

Indirect Measurement Using Similar Triangles
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.
Two common ways to achieve indirect measurement involve
(1) using a mirror on the ground and
(2) using shadow lengths and find an object’s height.
Method 1 measures the person’s height and the distances between the person, mirror, and object.
Method 2 measures shadows and the person’s height.

Indirect Measurement: Examples
How to apply your knowledge of similar triangles and proportions to model real-life situations and to find unknown measurements indirectly.

  1. A tree outside Ellie’s building casts a 125 foot shadow. At the same time of day, Ellie casts a 5.5 foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree?
  2. Cameron is 5 ft tall and casts a 12 ft shadow. At the same time of day, a nearby building casts a 78 ft shadow. How tall is the building?
  3. The Empire State Building is 1250 ft. tall. At 3:00, Pablo stands next to the building and has an 8 ft. shadow. If he is 6 ft tall, how long is the Empire State Building’s shadow at 3:00?

Indirect Measurement Using Similar Triangles
Indirect measurement of stadium lights using similar triangles with 3 methods: a mirror, a shadow, and a photograph.

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