Indirect measure

Front

What is an indirect measure?

Back

An indirect measure is a method used to determine the size or height of an object without measuring it directly, often using proportions or similar figures.

Front

How do you set up a proportion for indirect measurement?

Back

To set up a proportion, compare the ratios of corresponding sides of similar figures. For example, if a tree's height and shadow length are known, you can set up a ratio with the unknown height and its shadow length.

Front

If a tree is 72 feet tall and casts a shadow of 12 feet, what is the height of a tree that casts a shadow of 5 feet?

Back

30 feet.

Front

What does it mean for figures to be similar?

Back

Similar figures have the same shape but may differ in size. Their corresponding angles are equal, and their sides are proportional.

Front

If a tree is 12 feet tall and casts a shadow of 9 feet, how tall is a building that casts a shadow of 24 feet?

Back

32 feet.

Front

What is the formula for finding the height of an object using shadows?

Back

Height of object 1 / Shadow length of object 1 = Height of object 2 / Shadow length of object 2.

Front

What is the height of a pine tree if you can see its top in a mirror placed on the ground?

Back

72 feet.

Front

True or False: The sides of similar figures must be proportional.

Back

True.

Front

What is the relationship between the lengths of shadows and the heights of objects?

Back

The lengths of shadows are proportional to the heights of the objects casting them.

Front

If a tree's shadow is 12 feet long and the tree is 72 feet tall, what is the ratio of height to shadow length?

Back

The ratio is 72:12, which simplifies to 6:1.