Nested Triangles

Front

What is a nested triangle?

Back

A nested triangle is a triangle that is contained within another triangle, sharing the same vertex and angles.

Front

How do you find the height of an object using similar triangles?

Back

You can use the ratio of the heights to the lengths of the shadows to find the height of an object. If two triangles are similar, the ratios of their corresponding sides are equal.

Front

If a statue is 8 feet tall and casts a 6-foot shadow, what is the ratio of height to shadow length?

Back

The ratio is 8:6, which simplifies to 4:3.

Front

If a tree casts a shadow that is 24 feet long, how can you find its height using the statue's shadow?

Back

Set up a proportion using the known height and shadow length of the statue to find the height of the tree.

Front

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

Back

Height of object = (Height of known object / Length of known shadow) * Length of unknown shadow.

Front

If a 6-foot person casts a 4-foot shadow, what is the height of a building that casts a 60-foot shadow?

Back

Using the ratio, the height of the building is 90 feet.

Front

What is the scale factor in the flagpole problem where 1 inch represents 4 feet?

Back

The scale factor is 4 feet per 1 inch.

Front

If a flagpole measures 12 inches, how tall is the actual pole?

Back

The actual height is 48 feet (12 inches * 4 feet/inch).

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 the same.

Front

How do you set up a proportion to solve for an unknown height?

Back

Set up the proportion as (height of known object / length of known shadow) = (height of unknown object / length of unknown shadow).