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

Q1:

Find the length of 𝐴 𝐢 .

Q2:

Consider triangle 𝐴 𝐡 𝐢 .

Find, in the form 1 :  π‘₯ , the ratio of the side lengths 𝐡 𝐢  :  𝐴 𝐡 .

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

Find, in the form 1 :  π‘₯ , the ratio of the side lengths 𝐡 𝐢  :  𝐴 𝐢 .

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

Q3:

Find the length of 𝐡 𝐢 in the figure to two decimal places.

Q4:

Find the values of π‘Ž and 𝑏 .

  • A π‘Ž = 3 , 𝑏 = 3 √ 6
  • B π‘Ž = 6 √ 3 , 𝑏 = 6
  • C π‘Ž = 3 √ 6 , 𝑏 = 3
  • D π‘Ž = 6 , 𝑏 = 6 √ 3
  • E π‘Ž = 6 , 𝑏 = 3 √ 6

Q5:

In triangle 𝐴 𝐡 𝐢 , the length of 𝐡 𝐢 is π‘₯ .

Find, in terms of π‘₯ , the length of 𝐴 𝐢 .

  • A π‘₯ 2
  • B π‘₯
  • C 2 √ π‘₯
  • D 2 π‘₯
  • E √ π‘₯ 2

Find, in terms of π‘₯ , the length of 𝐴 𝐡 .

  • A √ 3 π‘₯
  • B 3 π‘₯
  • C π‘₯ √ 3
  • D π‘₯ 3
  • E √ 3 2 π‘₯

Q6:

Given a right triangle in which angle measures , which of the following is equal to the length of the side opposite to angle ?

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

Q7:

Given that 𝐴 𝐸 = 4 2 c m , and 𝐡 𝐷 is a median in β–³ 𝐴 𝐡 𝐢 , find the perimeter of β–³ 𝐴 𝐡 𝐷 .

Q8:

Find the value of π‘₯ in the given figure.

Q9:

Find the length of 𝐴 𝐡 .

Q10:

Find the lengths of 𝐡 𝐷 and 𝐷 𝐸 .

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