Trigonometric Ratios: Master the Basics with Interactive Quizzes

Question 1

In a right-angled triangle with an angle of 30 degrees, the value of cosine is:

Accepted Answer

1/2

Answer

1/4

Answer

2/3

Answer

1/6

Question 2

The trigonometric ratio that represents the length of the hypotenuse divided by the length of the adjacent side is:

Accepted Answer

Secant

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 3

The expression that is equivalent to 1/sin is:

Accepted Answer

Cosecant

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 4

The trigonometric ratio that is used to find the length of the side opposite the known angle in a right-angled triangle is:

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 5

In a right-angled triangle, the side adjacent to the angle of elevation is known as the:

Accepted Answer

Adjacent side

Answer

Opposite side

Answer

Cotangent side

Answer

Hypotenuse

Question 6

The trigonometric ratio that represents the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle is known as the:

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 7

Which trigonometric ratio represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle?

Accepted Answer

Cosine

Answer

Tangent

Answer

Sine

Answer

Cosecant

Question 8

The angle of depression from a window 50 m high to the base of a building is 30 degrees. Determine the horizontal distance between the window and the base of the building.

Accepted Answer

100 m

Answer

150 m

Answer

50 m

Answer

200 m

Question 9

The trigonometric ratio that represents the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle is:

Accepted Answer

Tangent

Answer

Cotangent

Answer

Sine

Answer

Cosine

Question 10

The cosine ratio is defined as the ratio of which two sides of a right-angled triangle?

Accepted Answer

Adjacent side / Hypotenuse

Answer

Opposite side / Hypotenuse

Answer

Opposite side / Adjacent side

Answer

Hypotenuse / Opposite side

Question 11

A ladder leans against a vertical wall, forming a right-angled triangle. The base of the ladder is 6 meters from the wall, and the top of the ladder is 8 meters above the ground. What is the sine of the angle between the ladder and the ground?

Accepted Answer

8/10

Answer

4/3

Answer

6/10

Answer

3/4

Question 12

Which of the following is NOT a trigonometric ratio?

Accepted Answer

Pythagorean theorem

Answer

Cosine

Answer

Sine

Question 13

The secant of an angle is equal to the ratio of which two sides of a right-angled triangle?

Accepted Answer

Hypotenuse / Adjacent

Answer

Adjacent / Hypotenuse

Answer

Opposite / Adjacent

Answer

Opposite / Hypotenuse

Question 14

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

Accepted Answer

Sine

Answer

Cosecant

Answer

Tangent

Answer

Cosine

Question 15

If the angle in a right-angled triangle is 30 degrees and the length of the opposite side is 5 cm, what is the length of the hypotenuse?

Accepted Answer

10 cm

Answer

5√2 cm

Answer

5 cm

Answer

5√3 cm

Question 16

Which trigonometric ratio is the reciprocal of the cosine?

Accepted Answer

Secant

Answer

Tangent

Answer

Cotangent

Answer

Cosecant

Question 17

In a right-angled triangle with an angle of elevation of 45 degrees and a height of 10 m, what is the length of the hypotenuse?

Accepted Answer

10√2 m

Answer

5√2 m

Answer

10 m

Answer

5 m

Question 18

Which of the following is NOT a Pythagorean identity?

Accepted Answer

Sin²θ + Cos²θ = 1/2

Answer

Tan²θ + 1 = Sec²θ

Answer

Sin²θ + Cos²θ = 1

Answer

Cot²θ + 1 = Csc²θ

Question 19

If the cosine of an angle in a right-angled triangle is 0.6, what is the value of the sine of that angle?

Accepted Answer

0.8

Answer

0.4

Answer

0.6

Answer

0.5

Question 20

Which trigonometric ratio represents the ratio of the length of the opposite side to the length of the adjacent side?

Accepted Answer

Tangent

Answer

Cosine

Answer

Secant

Answer

Sine

Question 21

In a right-angled triangle, if the length of the hypotenuse is 13 cm and the length of the opposite side is 5 cm, what is the length of the adjacent side?

Accepted Answer

12 cm

Answer

5 cm

Answer

7 cm

Answer

13 cm

Question 22

Which trigonometric identity is used to solve for the unknown side of a right-angled triangle?

Accepted Answer

Pythagorean theorem

Answer

Sine rule

Answer

Cosine rule

Answer

Area of a triangle

Question 23

If the angle of depression from the top of a tower to a car on the ground is 30 degrees and the height of the tower is 20 m, what is the horizontal distance between the tower and the car?

Accepted Answer

20√3 m

Answer

10√3 m

Answer

20 m

Answer

10 m