Worksheet: Trigonometric Ratios of Special Triangles

In this worksheet, we will practice how to find the side lengths of 45-45-90 and 30-60-90 triangles using trigonometric ratios.


A ladder 8 meters long leans against a wall. Find the horizontal length between the base of the ladder and the wall given the angle between the ladder and the ground is 45.

  • A28 m
  • B4 m
  • C42 m
  • D43 m
  • E833 m


Find, in terms of 𝑥, the length of the hypotenuse of this triangle.

  • A𝑥2
  • B𝑥2
  • C2𝑥
  • D2𝑥
  • E2𝑥


In the figure, the length of 𝐴𝐵 is 8.

Find the length of 𝐵𝐶.

  • A4
  • B8
  • C16
  • D2
  • E8

Given that the length of 𝐷𝐸 is 6, find the length of 𝐶𝐸. Give an exact answer.

  • A2
  • B22
  • C32
  • D2
  • E4


Use the figure to find the value of 𝑥.

  • A53 meters
  • B102 meters
  • C10 meters
  • D52 meters
  • E103 meters


Given that 𝐴𝐵=3, find 𝐵𝐶. Give an exact answer.

  • A32
  • B6
  • C3
  • D6
  • E23


Find the ratio of the length of 𝐴𝐵 to the length of 𝐵𝐶 in its simplest form.

  • A14:
  • B122:
  • C12:
  • D12:
  • E11:

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