Lesson Worksheet: Special Right Triangles Mathematics • 11th Grade

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 π‘₯ in the given figure.

Q2:

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

Q3:

Find the length of 𝐴𝐢.

Q4:

Find the values of π‘Ž and 𝑏.

  • Aπ‘Ž=3√6, 𝑏=3
  • Bπ‘Ž=6, 𝑏=3√6
  • Cπ‘Ž=6, 𝑏=6√3
  • Dπ‘Ž=6√3, 𝑏=6
  • Eπ‘Ž=3, 𝑏=3√6

Q5:

Find the length of 𝐴𝐡.

Q6:

Consider triangle 𝐴𝐡𝐢.

Find, in the form 1 : π‘₯, the ratio of the side lengths 𝐡𝐢 : 𝐴𝐡.

  • A1 : 2
  • B1 :β€‰βˆš3
  • C1 :  3
  • D1 :  1
  • E1 :β€‰βˆš2

Find, in the form 1 : π‘₯, the ratio of the side lengths 𝐡𝐢 : 𝐴𝐢.

  • A1 : 1
  • B1 : 2
  • C1 : 3
  • D1 :β€‰βˆš3
  • E1 :β€‰βˆš2

Q7:

In triangle 𝐴𝐡𝐢, the length of 𝐡𝐢 is π‘₯.

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

  • A2√π‘₯
  • B√π‘₯2
  • Cπ‘₯2
  • D2π‘₯
  • Eπ‘₯

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

  • A√3π‘₯
  • B3π‘₯
  • C√32π‘₯
  • Dπ‘₯√3
  • Eπ‘₯3

Q8:

Given that 𝐴𝐸=42cm, and 𝐡𝐷 is a median in △𝐴𝐡𝐢, find the perimeter of △𝐴𝐡𝐷.

Q9:

Find the lengths of 𝐡𝐷 and 𝐷𝐸.

  • A𝐡𝐷=73.95cm, 𝐷𝐸=37cm
  • B𝐡𝐷=32.87cm, 𝐷𝐸=10.96cm
  • C𝐡𝐷=49.3cm, 𝐷𝐸=24.65cm
  • D𝐡𝐷=59.16cm, 𝐷𝐸=19.72cm

Q10:

Given a right triangle 𝐴𝐡𝐢, 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

This lesson includes 8 additional questions and 108 additional question variations for subscribers.

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