Indirect Measurement

Front

What is Indirect Measurement?

Back

Indirect measurement is a technique used to measure an object that is difficult to measure directly by using proportions and similar triangles.

Front

What is a proportion in mathematics?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you set up a proportion for indirect measurement?

Back

To set up a proportion, you compare the height of an object to its shadow length with the height of a person to their shadow length.

Front

If a tower is 34 feet tall and casts a shadow of 10 feet, what is the ratio of height to shadow length?

Back

The ratio is 34:10 or simplified to 17:5.

Front

How can you find the height of a person using indirect measurement?

Back

By setting up a proportion using the height of the tower and the length of its shadow compared to the person's shadow.

Front

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

Back

Height of object / Length of shadow = Height of person / Length of person's shadow.

Front

If a person casts a shadow of 5 feet next to a tower that is 34 feet tall, how tall is the person?

Back

The person is 17 feet tall.

Front

What is the significance of using a mirror in indirect measurement?

Back

Using a mirror allows you to see the top of a tall object and create a right triangle to measure its height indirectly.

Front

If you see the top of a tree in a mirror placed 36 feet away, and the mirror is 6 feet tall, how tall is the tree?

Back

The tree is 72 feet tall.

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.