Lesson Worksheet: Special Right Triangles Mathematics • 11th Grade

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In this worksheet, we will practice finding lengths in 30-60-90-degree and in 45-45-90-degree triangles without trigonometry.

Q1:

Find the value of 𝑥 in the given figure.

Q2:

Find the length of 𝐵𝐶 in the figure to two decimal places.

Q3:

Find the length of 𝐴𝐶.

Q4:

Find the values of 𝑎 and 𝑏.

  • A𝑎=3√6, 𝑏=3
  • B𝑎=6, 𝑏=3√6
  • C𝑎=6, 𝑏=6√3
  • D𝑎=6√3, 𝑏=6
  • E𝑎=3, 𝑏=3√6

Q5:

Find the length of 𝐴𝐵.

Q6:

Consider triangle 𝐴𝐵𝐶.

Find, in the form 1 : 𝑥, the ratio of the side lengths 𝐵𝐶 : 𝐴𝐵.

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

Find, in the form 1 : 𝑥, the ratio of the side lengths 𝐵𝐶 : 𝐴𝐶.

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

Q7:

In triangle 𝐴𝐵𝐶, the length of 𝐵𝐶 is 𝑥.

Find, in terms of 𝑥, the length of 𝐴𝐶.

  • A2√𝑥
  • B√𝑥2
  • C𝑥2
  • D2𝑥
  • E𝑥

Find, in terms of 𝑥, the length of 𝐴𝐵.

  • A√3𝑥
  • B3𝑥
  • C√32𝑥
  • D𝑥√3
  • E𝑥3

Q8:

Given that 𝐴𝐸=42cm, and 𝐵𝐷 is a median in △𝐴𝐵𝐶, find the perimeter of △𝐴𝐵𝐷.

Q9:

Find the lengths of 𝐵𝐷 and 𝐷𝐸.

  • A𝐵𝐷=73.95cm, 𝐷𝐸=37cm
  • B𝐵𝐷=32.87cm, 𝐷𝐸=10.96cm
  • C𝐵𝐷=49.3cm, 𝐷𝐸=24.65cm
  • D𝐵𝐷=59.16cm, 𝐷𝐸=19.72cm

Q10:

Given a right triangle 𝐴𝐵𝐶, in which angle 𝐴 measures 30∘, which of the following is equal to the length of the side opposite angle 𝐴?

  • AThe length of the hypotenuse
  • BOne-third the length of the hypotenuse
  • CHalf the length of the side opposite the angle measuring 60∘
  • DHalf the length of the hypotenuse

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