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.

Tags

CCSS.7.G.B.4

Front

How can a mirror be used to measure the height of a tree?

Back

By standing at a distance from the tree and using a mirror on the ground, you can see the top of the tree reflected in the mirror. The angles formed create similar triangles, allowing you to calculate the height of the tree.

Front

What is the principle of similar triangles?

Back

The principle of similar triangles states that if two triangles have the same shape, their corresponding sides are in proportion.

Tags

CCSS.HSG.SRT.A.2

Front

If a person is 6 feet tall and stands 30 feet away from a tree, how can you find the height of the tree using indirect measurement?

Back

You can set up a proportion using the height of the person and the distance from the tree to find the height of the tree.

Tags

CCSS.HSG.SRT.C.8

Front

What is the formula for finding the height of an object using indirect measurement?

Back

Height = (Height of observer) * (Distance to object) / (Distance to observer) or using similar triangles.

Tags

CCSS.HSG.SRT.C.8

Front

What is the height of a tree if a 6-foot tall person standing 20 feet away sees the top of the tree in a mirror placed 10 feet away from the base of the tree?

Back

Height of the tree = (6 ft * 20 ft) / 10 ft = 12 ft.

Tags

CCSS.HSG.SRT.B.4

Front

What is the importance of angles in indirect measurement?

Back

Angles help establish relationships between the heights and distances of objects, allowing for the use of trigonometric ratios or similar triangles.

Tags

CCSS.HSG.CO.C.11

Front

What is a practical application of indirect measurement?

Back

Indirect measurement can be used in surveying land, determining the height of buildings, or measuring tall trees without climbing.

Tags

CCSS.HSG.SRT.C.8

Front

How does the height of the observer affect the measurement?

Back

The height of the observer must be accounted for in calculations, as it affects the proportion used to determine the height of the object.

Tags

CCSS.2.MD.A.3

Front

What is the relationship between the height of an object and the distance from the observer in indirect measurement?

Back

The height of the object is proportional to the distance from the observer, based on the principles of similar triangles.

Tags

CCSS.HSG.SRT.C.8