Grade 10 SOHCAHTOA: Right Triangles & Missing Angles

A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and the base is 6 feet from the wall, what is the angle between the ladder and the ground?

• 30 degrees

• 75 degrees

• 53.13 degrees

• 90 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?

• 7 feet

• 12 feet

• 10 feet

• 5√3 feet

A right triangle has one angle measuring 45 degrees. If the length of the adjacent side is 8 meters, what is the length of the opposite side?

• 8 meters

• 12 meters

• 10 meters

• 6 meters

A ramp is built to allow access to a building. If the ramp makes a 20-degree angle with the ground and is 12 feet long, how high does the ramp reach?

• 4.10 feet

• 3.5 feet

• 5.2 feet

• 6.0 feet

A surveyor measures a 50-meter distance from a point on the ground to the top of a hill. If the angle of elevation to the top of the hill is 35 degrees, how high is the hill?

• 25.5 meters

• 60 meters

• 35.01 meters

• 45 meters

A kite is flying at a height of 30 meters. If the string makes a 60-degree angle with the ground, how long is the string?

• 15 meters

• 20√3 meters

• 25√2 meters

• 30 meters

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

• 5.77 cm

• 7.5 cm

• 10 cm

• 3.5 cm

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

• 10 cm

• 6.5 cm

• 7.5 cm

• 5 cm

A boat is anchored 20 meters from the shore. If the angle of elevation from the boat to the top of a cliff is 75 degrees, how high is the cliff?

• 30 meters

• 74.64 meters

• 50 meters

• 90 meters