Indirect Measurement (2020-2021)

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 can mirrors be used in indirect measurement?

Back

Mirrors can be used to create a line of sight to the top of an object, allowing the observer to use similar triangles to calculate the object's height.

Front

What is the formula for similar triangles?

Back

If two triangles are similar, the ratios of their corresponding sides are equal. For example, if triangle A and triangle B are similar, then A1/A2 = B1/B2.

Front

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

Back

30 feet.

Front

What is the height of a building if it is determined to be 108 feet tall?

Back

108 feet.

Front

How do you solve for x in a proportion?

Back

Cross-multiply the terms and then isolate x. For example, if a/b = c/x, then a*x = b*c.

Front

What is the height of a flag if it is determined to be 15 feet tall?

Back

15 feet.

Front

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

Back

The height of an object is proportional to the length of its shadow when the angle of elevation of the sun is the same.

Front

What is the first step in solving an indirect measurement problem?

Back

Identify the similar triangles and set up a proportion based on their corresponding sides.

Front

If a tree's shadow is 12 feet long and the tree is 72 feet tall, what is the ratio of height to shadow length?

Back

The ratio is 72:12, which simplifies to 6:1.