Pythagoras and Trigonometry: Master Right-Angled Triangles

Question 1

What is the cosine ratio?

Accepted Answer

hypotenuse / adjacent

Answer

opposite / hypotenuse

Answer

adjacent / opposite

Answer

hypotenuse / opposite

Question 2

Which of the following is NOT a trigonometric function?

Accepted Answer

Quadratic

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 3

What is the inverse of the sine function?

Accepted Answer

Arc sine

Answer

Cosine

Answer

Tangent

Answer

Inverse sine

Question 4

In a right-angled triangle with sides a, b and c, where c is the hypotenuse, which of the following equations best represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

a - b = c

Answer

a/b = c

Question 5

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

1

Question 6

In a right-angled triangle, what is the name of the side opposite to the right angle?

Accepted Answer

Opposite side

Answer

Hypotenuse

Answer

Adjacent side

Question 7

Which formula represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Question 8

In a right-angled triangle with legs measuring 3 cm and 4 cm, find the length of the hypotenuse.

Accepted Answer

7 cm

Answer

5 cm

Answer

9 cm

Question 9

In a right-angled triangle, the side opposite the right angle is known as the:

Accepted Answer

Perpendicular

Answer

Hypotenuse

Answer

Base

Answer

Altitude

Question 10

Which trigonometric ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 11

Which of the following is the correct equation for the law of sines?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 12

A tree casts a shadow that is 15m long. The angle of elevation from the end of the shadow to the top of the tree is 30°. What is the height of the tree?

Accepted Answer

7.5m

Answer

15m

Answer

30m

Answer

45m

Question 13

Which of the following is the correct inverse trigonometric function for finding the angle θ when sin θ is known?

Accepted Answer

sin^-1 θ

Answer

cos^-1 θ

Answer

tan^-1 θ

Answer

cot^-1 θ

Question 14

Which of the following identities is always true for any angle θ?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tan²θ - 1 = sin²θ

Answer

cos²θ - sin²θ = 1

Answer

cot²θ - 1 = cos²θ

Question 15

What is the inverse trigonometric function of sin(θ)?

Accepted Answer

sin⁻¹(θ)

Answer

cos⁻¹(θ)

Answer

tan⁻¹(θ)

Answer

cot⁻¹(θ)

Question 16

Which of the following is NOT a property of similar triangles?

Accepted Answer

Corresponding perimeters are equal.

Answer

Corresponding angles are equal.

Answer

Corresponding sides are proportional.

Answer

Corresponding areas are proportional.

Question 17

Given that the sine of an angle is 0.5, determine the cosine of that same angle.

Accepted Answer

0.866

Answer

0.5

Answer

1

Answer

Cannot be determined

Question 18

In a right-angled triangle, the ratio of the sine of an angle to the cosine of the same angle is known as the:

Accepted Answer

Tangent

Answer

Cotangent

Answer

Secant

Answer

Cosecant

Question 19

Which of the following is the definition of a unit circle?

Accepted Answer

A circle with a radius of 1 unit

Answer

A circle with a diameter of 2 units

Answer

A circle inscribed in a square

Answer

A circle circumscribed around a square

Question 20

What is the value of sin(90 degrees)?

Accepted Answer

1

Answer

0

Answer

-1

Answer

Cannot be determined

Question 21

In a right-angled triangle, the side across from the right angle is known as the:

Accepted Answer

Opposite side

Answer

Adjacent side

Answer

Hypotenuse

Answer

Leg

Question 22

The Pythagorean theorem states:

Accepted Answer

a² + b² = c²

Answer

sin(θ) = opposite/hypotenuse

Answer

tan(θ) = opposite/adjacent

Answer

cos(θ) = adjacent/hypotenuse

Question 23

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

Accepted Answer

7 cm

Answer

12 cm

Answer

15 cm

Answer

Cannot be determined

Question 24

Which trigonometric identity is correct?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tan²θ + cot²θ = 1

Answer

sec²θ - 1 = tan²θ

Answer

csc²θ - 1 = cot²θ

Question 25

The area of a right-angled triangle is calculated as:

Accepted Answer

½ * base * height

Answer

½ * adjacent * opposite

Answer

base * height

Answer

adjacent * opposite

Question 26

In a right-angled triangle, which side is opposite the right angle?

Accepted Answer

Opposite side

Answer

Hypotenuse

Answer

Adjacent side

Answer

Long side

Question 27

In a right-angled triangle, which side is directly across from the right angle?

Accepted Answer

Opposite

Answer

Adjacent

Answer

Hypotenuse

Question 28

In a right-angled triangle, the length of the hypotenuse is 10 cm and the length of one leg is 6 cm. What is the length of the other leg?

Accepted Answer

8 cm

Answer

4 cm

Answer

12 cm

Answer

16 cm

Question 29

Which trigonometric ratio is used to find the length of the side opposite to a given angle in a right-angled triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 30

What is the value of sin(30°) in a right-angled triangle?

Accepted Answer

0.707

Answer

0.5

Answer

1

Answer

1.414

Question 31

In a right-angled triangle, the tangent of an angle is equal to the ratio of:

Accepted Answer

Opposite side to adjacent side

Answer

Adjacent side to opposite side

Answer

Hypotenuse to opposite side

Answer

Hypotenuse to adjacent side

Question 32

Which of the following is NOT a theorem or trigonometric formula?

Accepted Answer

Geometric mean theorem

Answer

Pythagoras theorem

Answer

Law of sines

Answer

Law of cosines

Question 33

Which quadrant does the angle -150° lie in?

Accepted Answer

Quadrant IV

Answer

Quadrant I

Answer

Quadrant II

Answer

Quadrant III

Question 34

What is the period of the function y = sin(x)?

Accepted Answer

2π

Answer

π

Answer

4π

Answer

6π

Question 35

Which of the following statements represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

2ab = c²

Answer

a - b = c

Question 36

Which trigonometric ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Question 37

What is the value of sin(30°) in a right-angled triangle?

Accepted Answer

½

Answer

0

Answer

1

Question 38

What is the value of cos(45°) in a right-angled triangle?

Accepted Answer

1/√2

Answer

√32

Answer

½

Question 39

What is the value of tan(60°) in a right-angled triangle?

Accepted Answer

√3

Answer

2

Answer

1

Question 40

What is the measure of angle θ in a right-angled triangle with sides of length 8 cm, 12 cm, and 13 cm?

Accepted Answer

36.87°

Answer

90°

Answer

45°

Question 41

What is the area of a right-angled triangle with sides of length 5 cm and 12 cm?

Accepted Answer

30 cm²

Answer

60 cm²

Answer

20 cm²

Question 42

Which of the following is the formula for the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² + a² = b²

Answer

c² - b² = a²

Question 43

What is the definition of the sine ratio?

Accepted Answer

Opposite side/Hypotenuse

Answer

Adjacent side/Hypotenuse

Answer

Adjacent side/Opposite side

Answer

Opposite side/Adjacent side

Question 44

Which of the following is not a trigonometric ratio?

Accepted Answer

Pythagorean ratio

Answer

Cosine ratio

Answer

Tangent ratio

Answer

Sine ratio

Question 45

What is the definition of the cosine ratio?

Accepted Answer

Adjacent side/Hypotenuse

Answer

Opposite side/Adjacent side

Answer

Adjacent side/Opposite side

Answer

Opposite side/Hypotenuse

Question 46

In a right-angled triangle, the statement that describes the relationship between the lengths of its sides is known as the:

Accepted Answer

Pythagoras' theorem

Answer

Algebraic theorem

Answer

Cosine theorem

Answer

Area theorem

Question 47

In a right-angled triangle, the square of the hypotenuse:

Accepted Answer

Is equal to the sum of the squares of the other two sides

Answer

Cannot be calculated

Answer

Is greater than the sum of the squares of the other two sides

Answer

Is less than the sum of the squares of the other two sides

Question 48

In a right-angled triangle, the tangent of an angle is defined as the ratio of:

Accepted Answer

Opposite side to adjacent side

Answer

Hypotenuse to opposite side

Answer

Adjacent side to opposite side

Question 49

Which of the following is the converse of the Pythagorean theorem?

Accepted Answer

If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled

Answer

If the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is right-angled

Question 50

A rectangular garden has a length of 10 m and a width of 8 m. What is the length of the diagonal of the garden?

Accepted Answer

12.8 m

Answer

10 m

Answer

20 m

Answer

15 m