Indirect Measurement

Front

What is Indirect Measurement?

Back

Indirect measurement is a technique used to measure an object without directly measuring it, often using similar triangles or proportions.

Front

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

Back

The formula is: (Height of Object 1 / Length of Shadow 1) = (Height of Object 2 / Length of Shadow 2).

Front

If a flagpole casts a shadow of 10 feet, and a 5-foot tall person casts a shadow of 2 feet, how tall is the flagpole?

Back

Using the formula: (Height of Flagpole / 10) = (5 / 2), the height of the flagpole is 25 feet.

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 to solve for a missing side in similar triangles?

Back

Set up the proportion by comparing the ratios of corresponding sides of the triangles.

Front

What is the height of a man who is 6 feet tall if his shadow is 2 feet long and a tree casts a shadow of 10 feet?

Back

Using the proportion: (6 / 2) = (Height of Tree / 10), the height of the tree is 30 feet.

Front

What is the significance of similar triangles in indirect measurement?

Back

Similar triangles allow us to use known measurements to find unknown measurements through proportional relationships.

Front

If a triangle has sides of 3 cm and 4 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(3² + 4²) = 5 cm.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

If a 10-foot tall tree casts a shadow of 5 feet, how long is the shadow of a 4-foot tall person?

Back

Using the proportion: (10 / 5) = (4 / x), the shadow of the person is 2 feet.