indirect measurement

Front

What is indirect measurement?

Back

Indirect measurement is a technique used to determine the height or distance of an object without directly measuring it, often using similar triangles or reflections.

Front

How do you set up a proportion for indirect measurement?

Back

To set up a proportion, compare the height of an object to its shadow length with another object's height and shadow length, forming a ratio: \( \frac{height_1}{shadow_1} = \frac{height_2}{shadow_2} \).

Front

If a fire hydrant is 2.5 feet tall and casts a 5-foot shadow, what is the height of a street light that casts a 26-foot shadow?

Back

The height of the street light is 13 feet.

Front

What is the formula to find the height of an object using shadows?

Back

The formula is: \( height = \frac{shadow_{object} \times height_{reference}}{shadow_{reference}} \).

Front

How can you find the height of a telephone pole using a person's height and shadow?

Back

Set up a proportion using the person's height and shadow compared to the pole's height and shadow.

Front

What is the height of a child who is 4 feet 6 inches tall if they cast a 6-foot shadow and a statue casts a 12-foot shadow?

Back

The height of the statue is 9 feet.

Front

What is the significance of similar triangles in indirect measurement?

Back

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

Front

How do you convert feet and inches to just feet for calculations?

Back

To convert, divide the inches by 12 and add to the feet. For example, 5 feet 8 inches = 5 + \( \frac{8}{12} \) = 5.67 feet.

Front

If a mirror is used to see the top of a tree, what principle is being applied?

Back

The principle of reflection and similar triangles is applied to determine the height of the tree indirectly.

Front

What is the height of a very tall pine tree if you see its top in a mirror and the distance from the mirror to you is equal to the height of the tree?

Back

The height of the tree is 72 feet.