Worksheet: Trigonometric Ratios of Special Triangles

In this worksheet, we will practice using the properties of a 45-45-90 triangle to find the lengths of the legs or the hypotenuse.

Q1:

A ladder 8 metres 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 4 5 .

  • A 4 m
  • B 4 3 m
  • C 8 3 3 m
  • D 4 2 m
  • E 2 8 m

Q2:

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

  • A 2 𝑥
  • B 2 𝑥
  • C 𝑥 2
  • D 𝑥 2
  • E 2 𝑥

Q3:

In the figure, the length of 𝐴 𝐵 is 8 .

Find the length of 𝐵 𝐶 .

  • A2
  • B8
  • C 8
  • D4
  • E16

Given that the length of 𝐷 𝐸 is 6, find the length of 𝐶 𝐸 . Give an exact answer.

  • A 2
  • B4
  • C 2 2
  • D 3 2
  • E2

Q4:

Use the figure to find the value of .

  • A metres
  • B metres
  • C metres
  • D metres
  • E 10 metres

Q5:

Given that 𝐴 𝐵 = 3 , find 𝐵 𝐶 . Give an exact answer.

  • A6
  • B3
  • C 2 3
  • D 3 2
  • E 6

Q6:

Find the ratio of the length of 𝐴 𝐵 to the length of 𝐵 𝐶 in its simplest form.

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

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