7.5a indirect measurement

Front

What is indirect measurement?

Back

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

Front

How do you set up a proportion for indirect measurement?

Back

To set up a proportion, you compare the ratios of the heights and shadows of two similar objects. For example, if Tree A's height/shadow = Tree B's height/shadow, you can solve for the unknown height.

Front

If a tree is 72 feet tall and casts a shadow of 12 feet, what is the height of a tree that casts a shadow of 5 feet?

Back

30 feet.

Front

What is the relationship between similar figures?

Back

Similar figures have the same shape but different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

If a flagpole is represented as 1 inch = 4 feet, how tall is a 12-inch flagpole?

Back

48 feet.

Front

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

Back

The height of the object can be found using the distance from the mirror to the observer and the distance from the mirror to the object, maintaining proportionality.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you use shadows to find the height of an object?

Back

By measuring the length of the shadow and using a known height and shadow length to set up a proportion.

Front

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

Back

32 feet.

Front

What is the importance of proportions in indirect measurement?

Back

Proportions allow us to relate the measurements of different objects to find unknown values based on known values.