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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?
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.
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At your school, which of the three objects casts the longest shadow?
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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?
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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?
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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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Description
This quiz covers concepts of indirect measurement using similar triangles, proportions, and practical applications like calculating heights from shadows. Solve problems related to sailboats, ladders, and other objects to enhance your understanding of geometric relationships.
