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Calculus > Right triangles & trigonometry > Flashcards

Right triangles & trigonometry Flashcards

1
Q

What is the Pythagorean theorem?

A

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

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2
Q

True or False: The hypotenuse is the longest side of a right triangle.

A

True

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3
Q

Fill in the blank: In a right triangle, the two legs are the sides that form the ______.

A

right angle

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4
Q

What is the formula for calculating the area of a right triangle?

A

Area = 1/2 * base * height

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5
Q

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

A

Sine

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6
Q

What is the sine of a 30-degree angle?

A

0.5

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7
Q

If the opposite side is 3 and the hypotenuse is 5, what is the sine of the angle?

A

0.6

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8
Q

True or False: Cosine is the ratio of the adjacent side to the hypotenuse.

A

True

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9
Q

What is the cosine of a 60-degree angle?

A

0.5

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10
Q

Fill in the blank: The tangent function is the ratio of the ______ side to the adjacent side.

A

opposite

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11
Q

What is the tangent of a 45-degree angle?

A

1

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12
Q

If the adjacent side is 4 and the opposite side is 3, what is the tangent of the angle?

A

0.75

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13
Q

What is the relationship between the angles in a right triangle?

A

The sum of the two acute angles is 90 degrees.

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14
Q

True or False: In a right triangle, the two legs can be of equal length.

A

True

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15
Q

What is the length of the hypotenuse in a right triangle with legs of length 3 and 4?

A

5

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16
Q

Fill in the blank: The sides of a 30-60-90 triangle are in the ratio of ______.

A

1 : √3 : 2

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17
Q

What is the inverse function of sine called?

A

Arcsine

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18
Q

What is the inverse function of cosine called?

A

Arccosine

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19
Q

What is the inverse function of tangent called?

A

Arctangent

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20
Q

If the angle is 30 degrees, what is the cosine value?

A

√3/2

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21
Q

True or False: The angles in a right triangle can be more than 90 degrees.

A

False

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22
Q

What is the length of one leg of a right triangle if the hypotenuse is 10 and the other leg is 6?

A

8

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23
Q

Fill in the blank: The Law of Cosines is used to find a side of a triangle when you know two sides and the ______.

A

included angle

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24
Q

What is the angle in a right triangle if the opposite side is 1 and the adjacent side is √3?

A

30 degrees

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25
Q

True or False: The side opposite the largest angle in a triangle is always the longest side.

A

True

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26
Q

What is the tangent of a 30-degree angle?

A

√3/3

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27
Q

Fill in the blank: The ratio of the lengths of the sides of a triangle is known as its ______.

A

proportions

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28
Q

If a right triangle has an angle of 45 degrees, what are the lengths of the legs?

A

Equal lengths

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29
Q

What is the area of a right triangle with a base of 5 and a height of 12?

A

30

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30
Q

Fill in the blank: The hypotenuse of a right triangle is always opposite the ______.

A

right angle

31
Q

What is the sine of a 90-degree angle?

32
Q

True or False: The sides of a triangle can never be 0.

33
Q

What is the cosine of a 30-degree angle?

34
Q

In a right triangle, if one angle measures 25 degrees, what is the other acute angle?

A

65 degrees

35
Q

Fill in the blank: The longest side of a right triangle is called the ______.

A

hypotenuse

36
Q

If the hypotenuse is 13 and one leg is 5, what is the other leg?

37
Q

What is the tangent of a 60-degree angle?

38
Q

True or False: In a right triangle, the lengths of the legs must be positive numbers.

39
Q

What is the formula for the Pythagorean theorem?

A

a² + b² = c²

40
Q

Fill in the blank: The angles in a triangle add up to ______ degrees.

41
Q

What is the sine of a 45-degree angle?

42
Q

What is the cosine of a 45-degree angle?

43
Q

If a right triangle has legs of lengths 7 and 24, what is the length of the hypotenuse?

44
Q

True or False: All angles in a right triangle are acute.

45
Q

What is the formula for finding the length of a leg given the hypotenuse and the other leg?

A

Leg = √(Hypotenuse² - Other Leg²)

46
Q

Fill in the blank: A right triangle with angles of 30, 60, and 90 degrees is known as a ______ triangle.

47
Q

What is the tangent of a 90-degree angle?

48
Q

If the opposite side is 5 and the adjacent side is 12, what is the tangent of the angle?

49
Q

True or False: The legs of a right triangle can be of different lengths.

50
Q

What is the sine of an angle if the opposite side is 8 and the hypotenuse is 10?

51
Q

Fill in the blank: The cosine of an angle is equal to the length of the ______ side divided by the length of the hypotenuse.

52
Q

What is the value of the sine of 0 degrees?

53
Q

What is the length of the adjacent side if the hypotenuse is 15 and the opposite side is 9?

54
Q

True or False: In a 45-45-90 triangle, the legs are equal.

55
Q

What is the area of a right triangle with legs of length 6 and 8?

56
Q

What is the cosine of a 90-degree angle?

57
Q

Fill in the blank: The formula for the Law of Sines is ______.

A

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

58
Q

What is the tangent of a 0-degree angle?

59
Q

If one leg of a right triangle is 9 and the hypotenuse is 15, what is the length of the other leg?

60
Q

True or False: The angles in a right triangle can be negative.

61
Q

What is the sine of 60 degrees?

62
Q

What is the cosine of 0 degrees?

63
Q

Fill in the blank: The tangent of an angle can be found using the formula ______.

A

opposite/adjacent

64
Q

What is the length of the hypotenuse if one leg is 7 and the other leg is 24?

65
Q

True or False: The Pythagorean theorem can only be used in right triangles.

66
Q

What is the sine of 45 degrees?

67
Q

What is the cosine of 30 degrees?

68
Q

Fill in the blank: The opposite side is opposite to the ______ of the angle.

69
Q

What is the area of a right triangle with a base of 10 and a height of 5?

70
Q

What is the tangent of 45 degrees?

71
Q

If the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

A

√64 or 8

72
Q

True or False: The angles in a triangle can exceed 180 degrees.

73
Q

What is the sine of 90 degrees?

Calculus (3 decks)

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