Real-Life Triangle Challenges: Pythagorean & Trig Ratios

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder is 10 feet long. How high up the wall does the ladder reach?

• 10 feet

• 6 feet

• 4 feet

• 8 feet

A right triangle has one leg measuring 8 cm and a hypotenuse measuring 10 cm. What is the length of the other leg?

• 5 cm

• 7 cm

• 9 cm

• 6 cm

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?

• 5√3 feet

• 10 feet

• 12 feet

• 7 feet

A ramp is built to help wheelchair access. If the ramp is 12 feet long and rises to a height of 4 feet, what is the angle of elevation of the ramp?

• 30.0 degrees

• 15.5 degrees

• 19.1 degrees

• 22.3 degrees

A kite is flying at a height of 30 meters. If the string of the kite makes an angle of 45 degrees with the ground, how far is the kite from the person holding the string?

• 50.00 meters

• 35.00 meters

• 25.00 meters

• 42.43 meters

A triangular park has sides measuring 5 m, 12 m, and 13 m. Is this triangle a right triangle?

• No, this triangle is an isosceles triangle.

• No, this triangle is not a right triangle.

• Yes, this triangle is an equilateral triangle.

• Yes, this triangle is a right triangle.

A 20-foot tall flagpole casts a shadow of 15 feet. What is the angle of elevation of the sun?

• 53.13 degrees

• 75 degrees

• 45 degrees

• 30 degrees

A right triangle has an angle of 60 degrees and an adjacent side measuring 5 cm. What is the length of the opposite side?

• 5 cm

• 10 cm

• 5√3 cm

• 3√3 cm

A boat is anchored 10 meters from the shore. If a line from the boat to a point on the shore makes a 30-degree angle with the shore, how far is the boat from that point on the shore?

• 5 meters

• 10 meters

• 15 meters

• 10√3 meters

A construction worker needs to determine the height of a building. He stands 50 meters away from the building and measures the angle of elevation to the top of the building as 60 degrees. How tall is the building?

• 75 meters

• 100 meters

• 50 meters

• 86.6 meters