Indirect Measurement in Geometry

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Questions and Answers

Indirect measurement uses _______ triangles to find the length of something.

similar

Which of the following proportions could be used to find x?

  • x/2 = 6/1.5 (correct)
  • x/3 = 4/2
  • x/5 = 10/2
  • x/4 = 8/2

In the lake, a sailboat casts a shadow of 4 yards. A buoy that is 2 feet tall casts a shadow of 1 foot. What is the height of the sailboat?

24 feet

A ladder is set up against a building. How far up does the ladder reach on the building? Round your answer to the nearest hundredth.

<p>6.67 m</p> Signup and view all the answers

At your school, which of the three objects casts the longest shadow?

<p>The tree (B)</p> Signup and view all the answers

Emily is 5 feet tall and casts a shadow of 28 inches. Miranda's shadow is 29.4 inches long. Approximately how tall is Miranda?

<p>5 1/4 feet</p> Signup and view all the answers

A tree casts a shadow of 28 feet. A biologist who is 7 feet tall casts a shadow of 2 feet. How tall is the tree?

<p>98 feet</p> Signup and view all the answers

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Study Notes

Indirect Measurement

  • Indirect measurement relies on similar triangles to determine lengths or heights that are not easily accessible.

Proportions in Measurement

  • The proportion x/2 = 6/1.5 can be effectively utilized to solve for an unknown value, x.

Sailboat Height Calculation

  • A sailboat casting a shadow of 4 yards can be calculated for height using a 2 feet tall buoy with a 1 foot shadow, resulting in a height of 24 feet for the sailboat.

Ladder Measurement

  • When a ladder is positioned against a building, it reaches approximately 6.67 meters up the wall; this value should be rounded to the nearest hundredth.

Shadow Comparison

  • Among three objects (a 20-foot tall building, a 252 inches tree, and a 6 yards flagpole), the tree is the one that casts the longest shadow.

Height Estimation with Shadows

  • Emily's height of 5 feet with a 28-inch shadow allows comparison with Miranda, who has a 29.4-inch shadow, estimating Miranda's height at about 5 1/4 feet.

Calculation of Tree Height

  • A tree casting a shadow of 28 feet indicates it measures 98 feet tall when compared to a biologist's height of 7 feet and his 2 feet shadow.

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