Indirect Measurement

Front

What is Indirect Measurement?

Back

Indirect measurement is a technique used to determine the height or distance of an object without measuring it directly, often 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. It is often used in indirect measurement to relate the dimensions of similar figures.

Front

How do you set up a proportion for indirect measurement?

Back

To set up a proportion, identify two similar triangles or figures, then create a ratio of corresponding sides. For example, if triangle A has a height of h1 and shadow s1, and triangle B has a height of h2 and shadow s2, the proportion is h1/s1 = h2/s2.

Front

If a tree is 12 feet tall and casts a shadow of 9 feet, what is the height of a building that casts a shadow of 24 feet?

Back

32 feet (Set up the proportion: 12/9 = h/24, solving gives h = 32 feet).

Front

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

Back

Height = (Height of object 1 / Shadow of object 1) * Shadow of object 2.

Front

If a tree casts a shadow of 15 feet and is 10 feet tall, what is the height of a building that casts a shadow of 30 feet?

Back

20 feet (Using the proportion: 10/15 = h/30, solving gives h = 20 feet).

Front

What is the significance of similar triangles in indirect measurement?

Back

Similar triangles have the same shape but different sizes, allowing us to use their proportional relationships to find unknown heights or distances.

Front

What is the height of a tree if it casts a shadow of 12 feet and the shadow of a nearby building is 36 feet, and the building is 30 feet tall?

Back

The height of the tree is 10 feet (Set up the proportion: 30/36 = h/12, solving gives h = 10 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 at the same angle.

Front

If a flagpole is 20 feet tall and casts a shadow of 5 feet, what is the height of a nearby tree that casts a shadow of 15 feet?

Back

60 feet (Using the proportion: 20/5 = h/15, solving gives h = 60 feet).