Worksheet: Properties of 30-60-90-Degree Triangles

In this worksheet, we will practice finding lengths in 30-60-90-degree triangles.

Q1:

Find the value of 𝑥 in the given figure.

Q2:

Find the length of 𝐵 𝐶 in the figure to two decimal places.

Q3:

Find the length of 𝐴 𝐶 .

Q4:

Find the values of 𝑎 and 𝑏 .

  • A 𝑎 = 3 , 𝑏 = 3 6
  • B 𝑎 = 6 3 , 𝑏 = 6
  • C 𝑎 = 3 6 , 𝑏 = 3
  • D 𝑎 = 6 , 𝑏 = 6 3
  • E 𝑎 = 6 , 𝑏 = 3 6

Q5:

Find the length of 𝐴 𝐵 .

Q6:

Consider triangle 𝐴 𝐵 𝐶 .

Find, in the form 1 :  𝑥 , the ratio of the side lengths 𝐵 𝐶  :  𝐴 𝐵 .

  • A1 :  1
  • B1 :  3
  • C1 :  2
  • D1 : 2
  • E1 :  3

Find, in the form 1 :  𝑥 , the ratio of the side lengths 𝐵 𝐶  :  𝐴 𝐶 .

  • A1 :  3
  • B1 :  2
  • C1 : 1
  • D1 : 2
  • E1 : 3

Q7:

In triangle 𝐴 𝐵 𝐶 , the length of 𝐵 𝐶 is 𝑥 .

Find, in terms of 𝑥 , the length of 𝐴 𝐶 .

  • A 𝑥 2
  • B 𝑥
  • C 2 𝑥
  • D 2 𝑥
  • E 𝑥 2

Find, in terms of 𝑥 , the length of 𝐴 𝐵 .

  • A 3 𝑥
  • B 3 𝑥
  • C 𝑥 3
  • D 𝑥 3
  • E 3 2 𝑥

Q8:

Given that 𝐴 𝐸 = 4 2 c m , and 𝐵 𝐷 is a median in 𝐴 𝐵 𝐶 , find the perimeter of 𝐴 𝐵 𝐷 .

Q9:

Find the lengths of 𝐵 𝐷 and 𝐷 𝐸 .

  • A 𝐵 𝐷 = 7 3 . 9 5 c m , 𝐷 𝐸 = 3 7 c m
  • B 𝐵 𝐷 = 3 2 . 8 7 c m , 𝐷 𝐸 = 1 0 . 9 6 c m
  • C 𝐵 𝐷 = 5 9 . 1 6 c m , 𝐷 𝐸 = 1 9 . 7 2 c m
  • D 𝐵 𝐷 = 4 9 . 3 c m , 𝐷 𝐸 = 2 4 . 6 5 c m

Q10:

Given a right-angled triangle 𝐴 𝐵 𝐶 in which angle 𝐴 measures 3 0 , which of the following is equal to the length of the side opposite to angle 𝐴 ?

  • A half the length of the side opposite to the angle measuring 6 0
  • B the length of the hypotenuse
  • C one-third the length of the hypotenuse
  • D half the length of the hypotenuse

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