Right Triangles: Solve Problems & Draw Diagrams

A ladder leans against a wall, forming a right triangle. If the ladder is 10 feet long and reaches a height of 8 feet on the wall, draw and label the triangle. What is the distance from the base of the wall to the bottom of the ladder?

• 4 feet

• 8 feet

• 10 feet

• 6 feet

Two similar right triangles are formed by a 5-foot tall tree casting a shadow of 4 feet. If a person is 6 feet tall, how long is their shadow? Draw and label both triangles.

• 5.2 feet

• 3.6 feet

• 6.4 feet

• 4.8 feet

A ramp is built to help wheelchair access. If the ramp is 12 feet long and rises 3 feet, draw and label the triangle. What is the horizontal distance from the base of the ramp to the wall?

• 9 feet

• 10 feet

• 12 feet

• Approximately 11.62 feet

In a park, a 3-foot tall statue casts a shadow of 2 feet. If a nearby building is 15 feet tall, how long is its shadow? Draw and label the triangles involved.

• 5 feet

• 12 feet

• 10 feet

• 8 feet

A right triangle has one angle measuring 30 degrees and the opposite side is 5 cm. Draw and label the triangle. What is the length of the hypotenuse?

• 10 cm

• 12 cm

• 8 cm

• 6 cm

A 6-foot tall flagpole casts a shadow of 4 feet. If a nearby tree is 9 feet tall, how long is its shadow? Draw and label the triangles to show the relationship.

• 6 feet

• 10 feet

• 8 feet

• 5 feet

A right triangle has legs measuring 8 cm and 6 cm. Draw and label the triangle. What is the length of the hypotenuse?

• 10 cm

• 12 cm

• 14 cm

• 8 cm

A 10-foot tall building casts a shadow of 5 feet. If a 15-foot tall tree is nearby, how long is its shadow? Draw and label both triangles to illustrate the similarity.

• 10 feet

• 7.5 feet

• 12 feet

• 5 feet

A right triangle has a base of 9 inches and a height of 12 inches. Draw and label the triangle. What is the length of the hypotenuse?

• 18 inches

• 10 inches

• 13 inches

• 15 inches

Two similar right triangles have corresponding sides in the ratio of 2:3. If one triangle has a base of 4 cm, what is the base of the larger triangle? Draw and label both triangles.

• 8 cm

• 6 cm

• 7 cm

• 5 cm