Angles and Trigonometry in Real-world Scenarios Quiz

Explore trigonometry with 15 questions on angles, triangles, and real-world scenarios. Test your skills and knowledge in practical applications.

#1

In a right triangle, which angle measures 90 degrees?

Opposite
Adjacent
Hypotenuse
None of the above
#2

What is the tangent of a 45-degree angle?

1
0
1/2
sqrt(3)/2
#3

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

90 degrees
180 degrees
270 degrees
360 degrees
#4

What is the sine of a 60-degree angle?

1/2
sqrt(3)/2
1
0
#5

What is the cosine of a 30-degree angle?

1/2
sqrt(3)/2
1
0
#6

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?

6 meters
12 meters
sqrt(12) meters
10 meters
#7

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?

30 degrees
45 degrees
60 degrees
75 degrees
#8

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
24 meters
6 meters
10 meters
#9

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?

4 meters
8 meters
16 meters
12 meters
#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 meters
12*sqrt(3) meters
24 meters
6*sqrt(3) meters
#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
24 meters
48 meters
sqrt(12) meters
#12

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

8 steps
10 steps
12 steps
14 steps
#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?

sqrt(3)/2 times its distance from the observer
2 times its distance from the observer
Its distance from the observer
sqrt(3) times its 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?

4 meters
4*sqrt(3) meters
8 meters
8*sqrt(3) meters
#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?

sqrt(3)/3 times its distance from the observer
3 times its distance from the observer
Its distance from the observer
sqrt(3) times its distance from the observer

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