Worksheet: Trigonometric Ratios of Special Triangles

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

Q1:

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∘.

  • A√28 m
  • B4 m
  • C4√2 m
  • D4√3 m
  • E8√33 m

Q2:

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

  • A𝑥√2
  • B𝑥√2
  • C2𝑥
  • D√2𝑥
  • E2√𝑥

Q3:

In the figure, the length of 𝐴𝐵 is √8.

Find the length of 𝐵𝐶.

  • A4
  • B8
  • C16
  • D2
  • E√8

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

  • A√2
  • B2√2
  • C3√2
  • D2
  • E4

Q4:

Use the figure to find the value of 𝑥.

  • A5√3 meters
  • B10√2 meters
  • C10 meters
  • D5√2 meters
  • E10√3 meters

Q5:

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

  • A3√2
  • B√6
  • C3
  • D6
  • E2√3

Q6:

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

  • A14:
  • B12√2:
  • C12:
  • D1√2:
  • E11:

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