SOH CAH TOA: Right Triangle Angle & Length Challenges

A ladder leans against a wall, forming a right triangle. If the base of the ladder is 4 feet from the wall and the ladder is 10 feet long, what is the angle between the ground and the ladder?

• 45 degrees

• 75 degrees

• 66.42 degrees

• 30 degrees

A tree casts a shadow that is 15 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30 degrees, how tall is the tree?

• 12 feet

• 5√3 feet

• 7 feet

• 10 feet

A right triangle has one angle measuring 45 degrees. If the length of the side opposite this angle is 5 cm, what is the length of the hypotenuse?

• 5 cm

• 7 cm

• 10 cm

• 5√2 cm

A ramp is built to allow access to a stage. If the ramp is 8 feet long and makes a 60-degree angle with the ground, how high does the ramp rise?

• 4√3 feet

• 6 feet

• 3 feet

• 5√3 feet

A kite is flying at a height of 20 meters. If the string makes a 40-degree angle with the ground, how long is the string?

• 15.50 meters

• 25.00 meters

• 31.11 meters

• 40.00 meters

A right triangle has one angle measuring 30 degrees and the adjacent side is 10 meters long. What is the length of the opposite side?

• 8.66 meters

• 12 meters

• 3.5 meters

• 5.77 meters

A person stands 50 meters away from a building and looks up at an angle of 70 degrees. How tall is the building?

• 200 meters

• 137.38 meters

• 100 meters

• 50 meters

A right triangle has a hypotenuse of 13 cm and one angle measuring 60 degrees. What is the length of the side opposite the 60-degree angle?

• 10 cm

• 12 cm

• 11.24 cm

• 9.5 cm

A flagpole casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. How tall is the flagpole?

• 5 meters

• 15 meters

• 10 meters

• 20 meters

A right triangle has an angle of 35 degrees and the adjacent side measures 12 meters. Calculate the length of the opposite side.

• 10.5 meters

• 6.2 meters

• 12.0 meters

• 8.4 meters