Indirect Measurement Task Cards

Front

What is indirect measurement?

Back

Indirect measurement is a technique used to determine the height or length of an object by using the properties of similar triangles or proportional relationships.

Front

How can shadows be used to measure height?

Back

Shadows can be used to measure height by comparing the length of the shadow to the height of the object, using the principle of similar triangles.

Front

If a 6-foot tall man casts a 9-foot shadow, what is the ratio of height to shadow length?

Back

The ratio of height to shadow length is 6:9, which simplifies to 2:3.

Front

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

Back

The formula is: Height of object / Length of shadow = Height of reference object / Length of reference shadow.

Front

If a statue is 10 feet tall and casts a 5-foot shadow, what is the height-to-shadow ratio?

Back

The height-to-shadow ratio is 10:5, which simplifies to 2:1.

Front

How do you find the height of an object if you know the height of a reference object and their shadow lengths?

Back

You can set up a proportion using the heights and shadow lengths of both objects and solve for the unknown height.

Front

What is the height of an object that casts a 12-foot shadow if a 4-foot tall object casts a 2-foot shadow?

Back

Using the proportion, the height of the object is 24 feet (4/2 = x/12, solving gives x = 24).

Front

What is the significance of similar triangles in indirect measurement?

Back

Similar triangles allow us to use proportional relationships to find unknown lengths or heights based on known measurements.

Front

If a cardboard box casts a 4-foot shadow and is 8 feet tall, what is the height-to-shadow ratio?

Back

The height-to-shadow ratio is 8:4, which simplifies to 2:1.

Front

What is the relationship between the height of an object and the length of its shadow?

Back

The relationship is proportional; as the height increases, the shadow length increases at a consistent ratio.