Learn Mode

Angles and Trigonometry in Real-world Scenarios Quiz

Go to Quiz Page

In a right triangle, which angle measures 90 degrees?

Hypotenuse

Explanation

Angle opposite the longest side.

What is the tangent of a 45-degree angle?

Explanation

Ratio of opposite side to adjacent side.

In a triangle, what is the sum of the interior angles?

360 degrees

Explanation

Total angle measure of a triangle.

What is the sine of a 60-degree angle?

sqrt(3)/2

Explanation

Ratio of opposite side to hypotenuse.

What is the cosine of a 30-degree angle?

sqrt(3)/2

Explanation

Ratio of adjacent side to hypotenuse.

A ladder is leaning against a wall. If the ladder forms a 30-degree angle with the ground and reaches a height of 6 meters up the wall, how long is the ladder?

10 meters

Explanation

Length of ladder = Height/sin(angle).

A ship travels 10 kilometers due east and then changes course to travel 15 kilometers due north. What is the bearing of the ship's new course from its starting point, to the nearest degree?

60 degrees

Explanation

Angle from due north to ship's new course.

A flagpole casts a shadow 12 meters long when the angle of elevation of the sun is 60 degrees. What is the height of the flagpole?

12 meters

Explanation

Height = Length of shadow * tan(angle).

A person walks 8 meters directly towards a lamppost, and the angle of elevation to the top of the lamppost is 30 degrees. How tall is the lamppost?

8 meters

Explanation

Height = Distance * tan(angle).

#10

A ladder is leaning against a wall. If the ladder forms a 60-degree angle with the ground and reaches a height of 12 meters up the wall, how long is the ladder?

12*sqrt(3) meters

Explanation

Length of ladder = Height/sin(angle).

#11

A tower casts a shadow that is 24 meters long when the angle of elevation of the sun is 30 degrees. What is the height of the tower?

12 meters

Explanation

Height = Length of shadow * tan(angle).

#12

A staircase has steps each 25 centimeters high. If a person climbs 2 meters vertically, how many steps will they have ascended?

14 steps

Explanation

Number of steps = Vertical distance / Step height.

#13

An observer on the ground looks up at a hot air balloon. When the angle of elevation to the balloon is 60 degrees, the balloon is directly overhead. What is the altitude of the balloon if it is flying at a constant height?

Its distance from the observer

Explanation

Altitude equals the distance from the observer.

#14

A ladder is leaning against a wall. If the ladder forms a 60-degree angle with the ground and the foot of the ladder is 4 meters away from the wall, how tall is the wall?

8 meters

Explanation

Height = Distance * tan(angle).

#15

An observer on the ground looks up at a hot air balloon. When the angle of elevation to the balloon is 75 degrees, the balloon is directly overhead. What is the altitude of the balloon if it is flying at a constant height?

Its distance from the observer

Explanation

Altitude equals the distance from the observer.

Angles and Trigonometry in Real-world Scenarios Quiz

In a right triangle, which angle measures 90 degrees?

What is the tangent of a 45-degree angle?

In a triangle, what is the sum of the interior angles?

What is the sine of a 60-degree angle?

What is the cosine of a 30-degree angle?

A ladder is leaning against a wall. If the ladder forms a 30-degree angle with the ground and reaches a height of 6 meters up the wall, how long is the ladder?

A ship travels 10 kilometers due east and then changes course to travel 15 kilometers due north. What is the bearing of the ship's new course from its starting point, to the nearest degree?

A flagpole casts a shadow 12 meters long when the angle of elevation of the sun is 60 degrees. What is the height of the flagpole?

A person walks 8 meters directly towards a lamppost, and the angle of elevation to the top of the lamppost is 30 degrees. How tall is the lamppost?

A ladder is leaning against a wall. If the ladder forms a 60-degree angle with the ground and reaches a height of 12 meters up the wall, how long is the ladder?

A tower casts a shadow that is 24 meters long when the angle of elevation of the sun is 30 degrees. What is the height of the tower?

A staircase has steps each 25 centimeters high. If a person climbs 2 meters vertically, how many steps will they have ascended?

An observer on the ground looks up at a hot air balloon. When the angle of elevation to the balloon is 60 degrees, the balloon is directly overhead. What is the altitude of the balloon if it is flying at a constant height?

A ladder is leaning against a wall. If the ladder forms a 60-degree angle with the ground and the foot of the ladder is 4 meters away from the wall, how tall is the wall?

An observer on the ground looks up at a hot air balloon. When the angle of elevation to the balloon is 75 degrees, the balloon is directly overhead. What is the altitude of the balloon if it is flying at a constant height?

Test Your Knowledge