Trigonometry Quizzes: Master the Basics of Triangles and Angles

Question 1

Which of the following is NOT a trigonometric ratio?

Accepted Answer

Radius

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 2

Which of the following is the correct formula for the area of a triangle?

Accepted Answer

½ × base × height

Answer

½ × base × (sin θ)

Answer

base × height

Answer

½ × (base × height) / sin θ

Question 3

Which of the following graphs represents the sine function?

Accepted Answer

A sinusoidal curve

Answer

A straight line

Answer

A circle

Answer

A parabola

Question 4

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

3π

Answer

4π

Question 5

In right-angled trigonometry, which ratio represents the relationship between the opposite side and the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 6

In a triangle with sides of length a, b, and c, the cosine rule can be expressed as:

Accepted Answer

a² = b² + c² - 2bc cos A

Answer

a² = b² - c² + 2bc cos A

Answer

a² + b² = c² - 2ab cos C

Answer

c² = a² + b² - 2ab cos C

Question 7

To calculate the area of a triangle using trigonometry, which formula should be employed?

Accepted Answer

Area = ½ * a * b * sin C

Answer

Area = (1/2) * base * height

Answer

Area = a² + b² - 2ab cos C

Answer

Area = a² + b² + 2ab cos C

Question 8

An observer stands 50 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, determine the height of the building.

Accepted Answer

25 meters

Answer

50 meters

Answer

100 meters

Answer

200 meters

Question 9

Which angle possesses the same sine value as 60 degrees?

Accepted Answer

120 degrees

Answer

30 degrees

Answer

45 degrees

Answer

150 degrees

Question 10

A ship navigates 100 km along a bearing of N30°E. Calculate the eastward distance covered by the ship.

Accepted Answer

57.3 km

Answer

86.6 km

Answer

100 km

Answer

115.5 km

Question 11

Find the unit vector in the direction of the vector (3, 4).

Accepted Answer

(3/5, 4/5)

Answer

(5/3, 5/4)

Answer

(4/3, 3/4)

Answer

(4/5, 3/5)

Question 12

In a right-angled triangle, what is the trigonometric ratio that represents the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 13

What is the value of sin 45°?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/5

Question 14

What is the value of cos 30°?

Accepted Answer

√3/2

Answer

1/2

Answer

1/3

Answer

√2/2

Question 15

What is the amplitude of the cosine function y = 3 cos 2x?

Accepted Answer

3

Answer

1

Answer

2

Answer

6

Question 16

Using the half-angle formula, find the value of cos(π/6).

Accepted Answer

0.866

Answer

0.5

Answer

1.0

Answer

1.732

Question 17

Find the unit vector in the direction of the vector A = (3, 4).

Accepted Answer

(3/5, 4/5)

Answer

(4/5, 3/5)

Answer

(5/3, 5/4)

Answer

(5/4, 5/3)

Question 18

Find the dot product of the vectors A = (1, 2) and B = (3, -4).

Accepted Answer

-5

Answer

5

Answer

10

Answer

-10

Question 19

Find the equation of the plane passing through the point (1, 2, 3) and perpendicular to the vector n = (2, 1, -1).

Accepted Answer

2x + y - z = 4

Answer

2x + y + z = 8

Answer

x + 2y - z = 7

Answer

x - 2y + z = 1

Question 20

In a right-angled triangle, the sine of an angle is:

Accepted Answer

Opposite side / Hypotenuse

Answer

Adjacent side / Hypotenuse

Answer

Hypotenuse / Opposite side

Answer

Hypotenuse / Adjacent side

Question 21

Which formula represents the cosine rule?

Accepted Answer

a² = b² + c² - 2bc cos A

Answer

a² + b² = c²

Answer

sin A / a = sin B / b = sin C / c

Answer

tan A = sin A / cos A

Question 22

What is the inverse function of the sine?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 23

What is the measure of each angle in an equilateral triangle?

Accepted Answer

60 degrees

Answer

30 degrees

Answer

45 degrees

Answer

90 degrees

Question 24

Which formula represents the cosine rule?

Accepted Answer

c^2 = a^2 + b^2 - 2ab * cos(C)

Answer

sin(A) / a = sin(B) / b

Answer

tan(A) = opposite / adjacent

Answer

Area = (1 / 2) * base * height

Question 25

Which formula represents the sine rule?

Accepted Answer

a / sin(A) = b / sin(B) = c / sin(C)

Answer

c^2 = a^2 + b^2 - 2ab * cos(C)

Answer

tan(A) = opposite / adjacent

Answer

Area = (1 / 2) * base * height

Question 26

Which formula represents the tangent rule?

Accepted Answer

tan((A - B) / 2) = (a - b) / (a + b)

Answer

sin(A) / a = sin(B) / b

Answer

Area = (1 / 2) * base * height

Answer

c^2 = a^2 + b^2 - 2ab * cos(C)

Question 27

Which formula represents the Pythagorean theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

sin(A) / a = sin(B) / b

Answer

c^2 = a^2 - b^2

Answer

tan(A) = opposite / adjacent

Question 28

Which formula represents the area of a triangle?

Accepted Answer

Area = (1 / 2) * base * height

Answer

tan(A) = opposite / adjacent

Answer

sin(A) / a = sin(B) / b

Answer

c^2 = a^2 + b^2 - 2ab * cos(C)

Question 29

A triangle has sides of length 7 cm, 8 cm, and 10 cm. What is the measure of the angle opposite the side of length 10 cm?

Accepted Answer

90°

Answer

30°

Answer

45°

Answer

60°

Question 30

What is the value of sin 30°?

Accepted Answer

0.5

Answer

1

Answer

√3/2

Answer

√2/2

Question 31

What is the value of cos 60°?

Accepted Answer

0.5

Answer

√3/2

Answer

1

Answer

√2/2

Question 32

A surveyor measures the angle of elevation to the top of a tower as 30°. If the surveyor is standing 50 meters from the base of the tower, what is the height of the tower?

Accepted Answer

28.87 meters

Answer

100 meters

Answer

57.74 meters

Answer

50 meters

Question 33

A ladder leans against a wall, making an angle of 60° with the ground. If the ladder is 5 meters long, how high up the wall does it reach?

Accepted Answer

4.33 meters

Answer

3.5 meters

Answer

5 meters

Answer

2.5 meters

Question 34

A triangle has sides of length 6 cm, 8 cm, and 10 cm. What is the measure of the largest angle in this triangle?

Accepted Answer

90°

Answer

60°

Answer

45°

Answer

120°

Question 35

Two ships leave a harbor at the same time. Ship A sails due east at 15 km/h, and Ship B sails due south at 20 km/h. What is the distance between the two ships after 3 hours?

Accepted Answer

39 km

Answer

30 km

Answer

55 km

Answer

45 km

Question 36

What is the value of sin(30°)?

Accepted Answer

0.5

Answer

√2/2

Answer

1

Answer

√3/2

Question 37

A triangle has sides of length 7 cm, 9 cm, and 11 cm. What is the area of this triangle?

Accepted Answer

30.98 cm² (approximately)

Answer

21 cm²

Answer

15.49 cm² (approximately)

Answer

42 cm²

Question 38

A ramp is 10 meters long and rises 2 meters vertically. What is the angle of inclination of the ramp?

Accepted Answer

11.54° (approximately)

Answer

9.58° (approximately)

Answer

21.8° (approximately)

Answer

18.43° (approximately)

Question 39

A surveyor measures the angle of depression from the top of a hill to a point on the ground as 15°. If the hill is 200 meters high, what is the horizontal distance from the base of the hill to the point on the ground?

Accepted Answer

746.4 meters (approximately)

Answer

200 meters

Answer

517.6 meters (approximately)

Answer

346.4 meters (approximately)

Question 40

Two sides of a triangle have lengths 12 cm and 15 cm, and the angle between them is 60°. What is the length of the third side?

Accepted Answer

13 cm (approximately)

Answer

15 cm

Answer

18 cm

Answer

9 cm