Right Triangle Problems in Trigonometry

Multiple choice questions right triangle problems related to trigonometry with answers at the bottom of the page.

  1. Question What is the measure of angle A in the right triangle below?

    right triangle question 1

    a) 17
    b) 27
    c) 17
    d) 90


  2. Question What is the value of x in the figure below?

    right triangle question 2

    a) 1
    b) 9
    c) 20
    d) 3


  3. Question In a right triangle, the measure of one of the angles is 49 and the hypotenuse has a length of 50 cm. Which of the following is the nearest approximation to the length, in cm, of the leg opposite to this angle?

    a) 32.8
    b) 57.5
    c) 37.7
    d) 30.3


  4. Question In the triangle ABC below, angle A measures 30 and the length of AC is 8 units. Find the length of BC

    right triangle question 4

    a) 8 / √ 3
    b) 4 / √ 3
    c) 4
    d) 8


  5. Question In the triangle below, what is sin α?

    right triangle question 5

    a) 13 / 9
    b) 9 / 13
    c) 13 √10 / 50
    d) 13 / 24


  6. Question Find the length of AC in the right triangle below.

    right triangle question 6

    a) 9
    b) 9 √2
    c) 18 √2
    d) 18


  7. Question Find the length of the hypotenuse in the right triangle below where x is a real number.

    right triangle question 7

    a) 5
    b) 10
    c) 25
    d) √ 5


  8. Question Find the area of a square whose diagonal is 40 meters.

    a) 80 m2
    b) 800 m2
    c) 1600 m2
    d) 40 m2


  9. Question In the figure below BC is perpendicular to AD, CD = 8, the measure of angle D is 60 and the measure of angle A is 45. Find the length of AB

    right triangle question 9

    a) 8 √6
    b) 8 √3
    c) 8 √2
    d) 8


  10. Question What is the length of AB in the figure below.

    right triangle question 10

    a) 12 √2
    b) 12
    c) 12 √3
    d) 12 √6


  11. Question In the figure below, find cosθ.

    right triangle question 12

    a) 3 / 5
    b) 4 / 5
    c) 1 / 5
    d) 2 / 5


  12. Question In the triangle below, m = ?

    right triangle question 13

    a) 5
    b) 10 √2
    c) 20 √2
    d) 5 √2


ANSWERS
  1. b)
  2. d)
  3. c)
  4. a)
  5. c)
  6. b)
  7. d)
  8. b)
  9. a)
  10. c)
  11. b)
  12. d)

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