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 directly measuring it, often using similar triangles or ratios.

Front

How can shadows be used to measure height?

Back

By comparing the length of a shadow to the height of an object, you can use proportions to find the height of another object with a known shadow length.

Front

If a 6-foot person casts a 2-foot shadow, what is the ratio of height to shadow length?

Back

The ratio is 6:2, which simplifies to 3:1.

Front

A flagpole casts a shadow of 10 feet while a 6-foot person casts a shadow of 2 feet. How tall is the flagpole?

Back

Using the ratio, the flagpole is 30 feet tall.

Front

What is the formula for finding height using similar triangles?

Back

Height = (Height of known object / Length of known object's shadow) * Length of unknown object's shadow.

Front

If a tree is 72 feet tall and has a shadow of 12 feet, what is the height of a tree with a 5-foot shadow?

Back

The height of the second tree is 30 feet.

Front

What is the scale factor in the problem where 1 inch equals 4 feet?

Back

The scale factor is 4 feet per inch.

Front

If a flagpole measures 12 inches, how tall is it in feet?

Back

The actual height is 48 feet.

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 when the light source is the same.

Front

How can mirrors be used to measure the height of tall objects?

Back

By placing a mirror on the ground and standing at a distance where you can see the top of the object in the mirror, you can use similar triangles to calculate the height.