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Lesson: Trigonometric Ratios of Special Triangles

In this lesson, we will learn how to use the properties of a 45-45-90 triangle to find the lengths of the legs or the hypotenuse.

Video

11:17

Sample Question Videos

05:54
04:30
03:50

Worksheet • 6 Questions • 3 Videos

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

Q2:

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

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

Q3:

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

Find the length of 𝐵 𝐶 .

  • A4
  • B16
  • C8
  • D √ 8
  • E2

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

  • A √ 2
  • B2
  • C 3 √ 2
  • D4
  • E 2 √ 2

Q4:

Use the figure to find the value of .

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

Q5:

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

  • A 3 √ 2
  • B √ 6
  • C3
  • D 2 √ 3
  • E6

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 4 :
  • C 1 2 √ 2 :
  • D 1 1 :
  • E 1 2 :
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