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.

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 2 8 m
  • B4 m
  • C 4 2 m
  • D 4 3 m
  • E 8 3 3 m

Q2:

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

  • A 𝑥 2
  • B 𝑥 2
  • C 2 𝑥
  • D 2 𝑥
  • E 2 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
  • B 2 2
  • C 3 2
  • D2
  • E4

Q4:

Use the figure to find the value of 𝑥.

  • A 5 3 meters
  • B 1 0 2 meters
  • C10 meters
  • D 5 2 meters
  • E 1 0 3 meters

Q5:

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

  • A 3 2
  • B 6
  • C3
  • D6
  • E 2 3

Q6:

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

  • A 1 4 :
  • B 1 2 2 :
  • C 1 2 :
  • D 1 2 :
  • E 1 1 :

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