Trigonometry Quizzes: Test Your Skills and Knowledge

Question 1

Two buildings stand 30 meters apart. The angle of elevation from one building's base to the top of the other is 45 degrees. Calculate the height of the taller building.

Accepted Answer

42.43 meters

Answer

30 meters

Answer

60 meters

Answer

84.85 meters

Question 2

In a triangle with sides a, b, and c, which formula represents the cosine rule?

Accepted Answer

a² = b² + c² - 2bc cos(A)

Answer

b² = a² + c² - 2ac cos(B)

Answer

c² = a² + b² - 2ab cos(C)

Answer

a² + b² = c² cos(A)

Question 3

A ladder leans against a wall. The ladder is 10 meters long, and its base is 6 meters from the wall. Calculate the angle between the ladder and the ground.

Accepted Answer

45 degrees

Answer

30 degrees

Answer

60 degrees

Answer

75 degrees

Question 4

Which of the following formulas represents the cosine rule?

Accepted Answer

a^2 = b^2 + c^2 - 2bc * cos(A)

Answer

a^2 + b^2 = c^2

Answer

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

Answer

cos(A) = b / c

Question 5

In a right-angled triangle, what type of angle is opposite the longest side?

Accepted Answer

Obtuse angle

Answer

Acute angle

Answer

Right angle

Answer

Cannot be determined

Question 6

Which formula represents the sine rule?

Accepted Answer

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

Answer

a^2 = b^2 + c^2

Answer

cos(A) = b / c

Answer

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

Question 7

In a healthcare setting, how could trigonometry be used to determine the angle of a patient's joint?

Accepted Answer

By measuring the length of the adjacent and opposite sides of the joint

Answer

By using a protractor

Answer

By using a ruler

Answer

By using a tape measure

Question 8

In a right-angled triangle, the ratio of the length of the side opposite to the angle to the length of the hypotenuse is known as the:

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 9

The area of a triangle with base 'b' and height 'h' can be calculated using the formula:

Accepted Answer

A = 1/2 * b * h

Answer

A = b * h

Answer

A = 1/2 * (b1 + b2) * h

Answer

A = sqrt(s(s-a)(s-b)(s-c))

Question 10

The sine rule relates the lengths of the sides of a triangle to the:

Accepted Answer

Angles

Answer

Area

Answer

Perimeter

Answer

Height

Question 11

The cosine rule can be used to find the:

Accepted Answer

Length of a side

Answer

Area of a triangle

Answer

Angle of a triangle

Answer

Height of a triangle

Question 12

The value of cos 30° is:

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

0

Question 13

Which trigonometric ratio represents the ratio of the side opposite to the angle to the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 14

Which of the following is an application of the cosine rule?

Accepted Answer

Finding the length of a missing side in a triangle

Answer

Calculating the area of a triangle

Answer

Determining if a triangle is right-angled

Answer

Measuring the angle of elevation of a building

Question 15

Which angle is complementary to a 30-degree angle?

Accepted Answer

90 degrees

Answer

45 degrees

Answer

60 degrees

Answer

120 degrees

Question 16

State the range of values for the sine of an angle.

Accepted Answer

[-1, 1]

Answer

[-∞, ∞]

Answer

[0, 1]

Answer

[1, ∞]

Question 17

In a right-angled triangle, the opposite side measures 5 cm and the hypotenuse measures 10 cm. Calculate the length of the adjacent side.

Accepted Answer

8 cm

Answer

5 cm

Answer

10 cm

Answer

12 cm

Question 18

What is the equivalent of 2π radians in degrees?

Accepted Answer

360 degrees

Answer

90 degrees

Answer

180 degrees

Answer

720 degrees

Question 19

Simplify the trigonometric expression: (sin θ + cos θ)²

Accepted Answer

1 + 2sin θ cos θ

Answer

1

Answer

sin² θ + cos² θ

Answer

sin² θ - cos² θ

Question 20

If the sine of an angle is 0.5, the cosine of the same angle is:

Accepted Answer

0.866

Answer

0.5

Answer

1

Answer

0

Question 21

An angle with a cosine of 0.6 corresponds to approximately:

Accepted Answer

53.13°

Answer

30°

Answer

60°

Answer

90°

Question 22

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

Accepted Answer

Opposite/Hypotenuse

Answer

Adjacent/Hypotenuse

Answer

Opposite/Adjacent

Answer

Hypotenuse/Opposite

Question 23

The area of a triangle with sides of length 5 cm, 7 cm, and 9 cm is:

Accepted Answer

28 cm²

Answer

14 cm²

Answer

21 cm²

Answer

35 cm²

Question 24

In healthcare, trigonometry can be used to calculate the angle of elevation of a patient's bed:

Accepted Answer

True

Answer

False

Question 25

A circle has a radius of 5cm. What is the length of the arc that subtends an angle of 60° at the center of the circle?

Accepted Answer

5π/3cm

Answer

10π/3cm

Answer

10π/2cm

Answer

5π/2cm

Question 26

In the field of healthcare, trigonometry can be utilized for:

Accepted Answer

Calculating the angle of a patient's limb to ensure accurate positioning.

Answer

Measuring the volume of a patient's medication.

Answer

Converting temperatures between Celsius and Fahrenheit.

Question 27

Which of the following is not considered a trigonometric function?

Accepted Answer

Exponent

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 28

What is the period of the sine function?

Accepted Answer

2π

Answer

4π

Answer

6π

Answer

π

Question 29

Which trigonometric identity is used to solve trigonometric equations?

Accepted Answer

sin²x + cos²x = 1

Answer

sin²x - cos²x = 1

Answer

cot²x - 1 = csc²x

Answer

tan²x + 1 = sec²x

Question 30

Which trigonometric ratio measures the length of the side opposite the angle divided by the length of the hypotenuse?

Accepted Answer

Sine

Answer

Tangent

Answer

Cosine

Answer

Cotangent

Question 31

Which formula correctly determines the area of a triangle using its base and height?

Accepted Answer

Area = (1/2) * base * height

Answer

Area = base * height

Answer

Area = (1/4) * base * height

Answer

Area = 2 * base * height

Question 32

Which trigonometric identity relates the sine and cosine of an angle?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tanθ = sinθ/cosθ

Answer

sinθ = 1/cosθ

Answer

cosθ = 1/sinθ

Question 33

In a right-angled triangle with a hypotenuse of 13 units and a side of length 5 units, what is the measure of the angle opposite the 5-unit side?

Accepted Answer

22.62 degrees (rounded to two decimal places)

Answer

60 degrees

Answer

45 degrees

Answer

30 degrees

Question 34

What is the sine rule formula?

Accepted Answer

a/sinA = b/sinB = c/sinC

Answer

a/tanA = b/tanB = c/tanC

Answer

a/cosA = b/cosB = c/cosC

Answer

a/cotA = b/cotB = c/cotC

Question 35

Which inverse trigonometric function returns the angle given the sine of the angle?

Accepted Answer

arcsin

Answer

arccot

Answer

arctan

Answer

arcos

Question 36

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

Accepted Answer

Sine

Answer

Secant

Answer

Cosine

Answer

Tangent

Question 37

Which formula is used to calculate the area of a triangle using the sine rule?

Accepted Answer

Area = (1/2) * a * b * sin(C)

Answer

Area = (1/2) * a * b * cos(C)

Answer

Area = (1/2) * b * c * sin(A)

Answer

Area = (1/2) * a * c * sin(B)

Question 38

What is the value of sin(90°) ?

Accepted Answer

1

Answer

0

Answer

1/2

Answer

-1

Question 39

Which function is the inverse of the cosine function?

Accepted Answer

Arccosine

Answer

Arcsecant

Answer

Arcsine

Answer

Arctangent

Question 40

In a triangle with sides a, b, c, and angle A opposite side a, the cosine rule states that:

Accepted Answer

c² = a² + b² - 2ab cos(A)

Answer

b² = c² + a² - 2ac cos(A)

Answer

c² = a² - b² - 2ab cos(A)

Answer

a² = b² + c² - 2bc cos(A)