Trigonometry Quiz

A ladder 10 ft long rests against a wall. If the foot of the ladder is 6 ft away from the wall, what angle does the ladder make with the ground?

• 36.87°

• 53.13°

• 45°

• 60°

An observer is standing 50 meters away from a building and sees the top of it at a 30° angle of elevation. What is the height of the building (ignore observer's height)?

• 25.0 m

• 28.9 m

• 30.0 m

• 50.0 m

A teacher wants to find the height of a tree using a clinometer. She measures an angle of elevation of 40° from a distance of 20 meters. What is the approximate height of the tree?

• 12.8 m

• 16.8 m

• 10.3 m

• 18.6 m

A ship sails due east and travels 40 km, then turns 30° north of east and travels another 60 km. What trigonometric function is best to find the ship's displacement from the starting point?

• Law of Sines

• Law of Cosines

• Tangent

• Sine Rule

A kite is flying at a height of 120 meters, and the string makes a 60° angle with the ground. What is the length of the string?

• 138.6 m

• 150.2 m

• 160.0 m

• 180.5 m

What trigonometric ratio is best used when determining the distance between two buildings using angles and the known height of one building?

• Cosine

• Tangent

• Sine

• Secant

A pole casts a shadow 5 meters long when the angle of elevation of the sun is 45°. What is the height of the pole?

• 5.0 m

• 6.0 m

• 7.5 m

• 10.0 m

A wheel of radius 50 cm rotates through an angle of 2 radians. What is the length of the arc formed?

• 100 cm

• 50 cm

• 25 cm

• 75 cm

In teaching navigation, a teacher explains how to find direction using bearings. Which trig function helps relate sides and angles in non-right triangles?

• Pythagorean theorem

• Law of Sines

• Tangent ratio

• Opposite-over-hypotenuse

A surveyor measures an angle of elevation of 25° to the top of a hill from a distance of 100 meters. What is the hill's height?

• 42.0 m

• 46.6 m

• 50.0 m

• 52.3 m