Similar Triangles Applications

Front

What are similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the principle of proportionality in similar triangles?

Back

The principle of proportionality states that in similar triangles, the ratios of the lengths of corresponding sides are equal.

Front

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

Back

To find the height of an object using similar triangles, set up a proportion between the height of the object and the length of its shadow, compared to the height of a reference object and its shadow.

Front

If a 2-meter tall person casts a shadow of 1 meter, what is the ratio of height to shadow length?

Back

The ratio is 2:1.

Front

A flagpole casts a shadow of 12 meters, and a 2-meter tall person casts a shadow of 1 meter. How tall is the flagpole?

Back

24 meters.

Front

A building casts a shadow of 50 meters, and a 4-meter tall person casts a shadow of 2 meters. How tall is the building?

Back

100 meters.

Front

What is the formula to calculate the height of an object using shadows?

Back

Height of object = (Height of reference object × Length of object's shadow) / Length of reference object's shadow.

Front

If a tree casts a shadow of 12 meters and a 2-meter tall person casts a shadow of 1.5 meters, how tall is the tree?

Back

16 meters.

Front

A building casts a shadow of 30 meters, and a 2-meter tall person casts a shadow of 1.5 meters. How tall is the building?

Back

40 meters.

Front

A building casts a shadow of 40 meters, and a 5-meter tall person casts a shadow of 2.5 meters. How tall is the building?

Back

100 meters.