Indirect Measurement

Front

What is indirect measurement?

Back

Indirect measurement is a technique used to determine the height or distance of an object by using the properties of similar triangles and ratios, rather than measuring directly.

Front

What are similar figures?

Back

Two objects that are the same shape but not the same size are called similar figures. They have proportional dimensions.

Front

How do you find the height of an object using shadows?

Back

To find the height of an object using shadows, you can set up a proportion between the height of the object and the length of its shadow compared to another object of known height and shadow length.

Front

If a 6-foot person casts a 2-foot shadow, and a flagpole casts a 10-foot shadow, how tall is the flagpole?

Back

30 feet.

Front

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

Back

Height of object 1 / Shadow of object 1 = Height of object 2 / Shadow of object 2.

Front

What is the height of a tree if a mirror is used to see its top and the distance from the mirror to the tree is known?

Back

The height of the tree can be calculated using the distance from the mirror and the angle of elevation to the top of the tree.

Front

What is the relationship between the angles of elevation and the heights of objects in indirect measurement?

Back

The angles of elevation from a point to the tops of objects can be used to create right triangles, allowing for the calculation of heights using trigonometric ratios.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

What is the height of a building if it is determined to be 108 feet through indirect measurement?

Back

108 feet.

Front

What is the significance of using mirrors in indirect measurement?

Back

Mirrors can help visualize angles of elevation and create similar triangles for calculating heights.