Exploring Triangle Similarities: Side Ratios in Action

A 5-foot tall person casts a shadow of 3 feet. At the same time, a tree casts a shadow of 12 feet. Are the triangles formed by the person and their shadow similar to the triangles formed by the tree and its shadow? Calculate the side ratios to prove it.

• Yes, the triangles are similar.

• The triangles are similar but only in area.

• The triangles are similar only if the heights are equal.

• No, the triangles are not similar.

In a park, a 4-meter tall statue casts a shadow of 2 meters. A nearby lamp post casts a shadow of 10 meters. Are the triangles formed by the statue and its shadow similar to the triangles formed by the lamp post and its shadow? What are the side ratios?

• Yes, the triangles are similar with a ratio of 4:5.

• No, the triangles are not similar.

• No, the triangles are similar with a ratio of 1:5.

• Yes, the triangles are similar with a ratio of 2:1.

Two buildings are standing next to each other. The first building is 30 meters tall and casts a shadow of 15 meters. The second building casts a shadow of 25 meters. If the triangles formed by the buildings and their shadows are similar, what is the height of the second building?

• 60 meters

• 40 meters

• 50 meters

• 35 meters

A 6-foot tall flagpole casts a shadow of 8 feet. A nearby 3-foot tall sign casts a shadow of 4 feet. Are the triangles formed by the flagpole and its shadow similar to the triangles formed by the sign and its shadow? Calculate the side ratios to confirm.

• No, the triangles are not similar.

• Yes, the triangles are similar.

• The triangles are similar only if the heights are equal.

• The triangles are similar but only in area.

A 10-meter tall tree casts a shadow of 5 meters. A nearby 2-meter tall bush casts a shadow of 1 meter. Are the triangles formed by the tree and its shadow similar to the triangles formed by the bush and its shadow? What are the side ratios?

• No, the triangles are not similar with a side ratio of 1.

• Yes, the triangles are similar with a side ratio of 3.

• Yes, the triangles are similar with a side ratio of 2.

• No, the triangles are similar but the side ratio is 0.5.

In a triangle, one angle measures 30 degrees, and the side opposite this angle is 4 cm. In a similar triangle, the corresponding angle is also 30 degrees, and the side opposite it is 8 cm. What is the ratio of the sides of the two triangles?

• 2:1

• 3:1

• 1:2

• 4:1

A ramp is 12 feet long and rises 3 feet. A second ramp is 16 feet long. If the two ramps are similar triangles, how high does the second ramp rise?

• 5 feet

• 6 feet

• 2 feet

• 4 feet

A 15-foot tall building casts a shadow of 10 feet. A 9-foot tall building casts a shadow of 6 feet. Are the triangles formed by the buildings and their shadows similar? Calculate the side ratios to prove it.

• The triangles are similar, but the ratios are incorrect.

• The triangles cannot be compared because they are different shapes.

• No, the triangles are not similar.

• Yes, the triangles are similar.

A 7-foot tall person casts a shadow of 4 feet. A 14-foot tall tree casts a shadow of 8 feet. Are the triangles formed by the person and their shadow similar to the triangles formed by the tree and its shadow? What are the side ratios?

• Yes, the triangles are similar with a side ratio of 4:7.

• No, the triangles are similar with a side ratio of 8:14.

• Yes, the triangles are similar with a side ratio of 7:4.

• No, the triangles are not similar with a side ratio of 14:8.

In a triangle, one angle measures 45 degrees, and the side opposite this angle is 5 cm. In a similar triangle, the corresponding angle is also 45 degrees, and the side opposite it is 10 cm. What is the ratio of the sides of the two triangles?

• 1:2

• 2:1

• 3:1

• 5:2