Lesson Worksheet: Trigonometric Ratios of Special Triangles Mathematics • 11th Grade

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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:

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

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

Q4:

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

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

Q5:

A flying kite is attached to a 90 m long string. Find the height of the kite if the angle between the string and the ground is 60∘.

  • A45√3 m
  • B45 m
  • C60√3 m
  • D180 m
  • E90√3 m

Q6:

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

  • A√3𝑥
  • B2𝑥√3
  • C2𝑥
  • D𝑥2
  • E√3𝑥2

Q7:

Given that 𝐴𝐵=2cm, find 𝐵𝐶. Give an exact answer.

  • A√3 cm
  • B2√3 cm
  • C2√3 cm
  • D1 cm
  • E4 cm

Q8:

Consider the rectangle in the following figure. If 𝐵𝐶=6cm and the measure of ∠𝐷𝐵𝐶=30∘, find the length of diagonal 𝐵𝐷.

  • A3 cm
  • B3√3 cm
  • C12 cm
  • D2√3 cm
  • E4√3 cm

Q9:

Given that 𝐴𝐵=1cm, find the area of triangle 𝐴𝐵𝐶.

  • A√34 cm2
  • B√33 cm2
  • C√3 cm2
  • D√32 cm2
  • E1 cm2

Q10:

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

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