Discovering Similar Triangles and Missing Sides

A ladder leans against a wall, forming a right triangle. If the ladder is 10 feet long and the wall is 8 feet high, how far is the base of the ladder from the wall?

• 10 feet

• 6 feet

• 8 feet

• 4 feet

Two trees cast shadows on the ground. Tree A is 15 feet tall and casts a shadow of 5 feet. Tree B casts a shadow of 10 feet. How tall is Tree B?

• 25 feet

• 35 feet

• 30 feet

• 20 feet

In a park, a triangular flower bed has a height of 4 feet and a base of 6 feet. If a similar flower bed has a height of 8 feet, what is the length of its base?

• 12 feet

• 10 feet

• 14 feet

• 16 feet

A right triangle has one angle measuring 30 degrees and a hypotenuse of 12 cm. What is the length of the side opposite the 30-degree angle?

• 10 cm

• 4 cm

• 8 cm

• 6 cm

A model of a building is made with similar triangles. If the model is 2 feet tall and the actual building is 50 feet tall, how long is the model if the actual building is 30 feet wide?

• 1.5 feet

• 3 feet

• 1.2 feet

• 4 feet

Two similar right triangles have side lengths in the ratio of 3:5. If the shorter side of the smaller triangle is 9 cm, what is the length of the shorter side of the larger triangle?

• 12 cm

• 20 cm

• 15 cm

• 18 cm

A flagpole casts a shadow of 12 feet. A nearby tree, which is similar in shape to the flagpole, casts a shadow of 18 feet. If the flagpole is 15 feet tall, how tall is the tree?

• 25 feet

• 18 feet

• 20 feet

• 22.5 feet

In a right triangle, if one leg measures 9 cm and the other leg is unknown, but the hypotenuse is 15 cm, what is the length of the unknown leg?

• 12 cm

• 14 cm

• 8 cm

• 10 cm

A triangular sail on a boat has a height of 5 meters and a base of 12 meters. If a similar sail is 10 meters tall, what is the length of its base?

• 15 meters

• 10 meters

• 20 meters

• 24 meters

A right triangle has sides measuring 6 cm and 8 cm. If a similar triangle has a hypotenuse of 10 cm, what are the lengths of the other two sides?

• 4 cm and 6 cm

• 6 cm and 8 cm

• 9 cm and 12 cm

• 5 cm and 7 cm