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

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


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.

  • A28 m
  • B4 m
  • C42 m
  • D43 m
  • E833 m


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

  • A𝑥2
  • B𝑥2
  • C2𝑥
  • D2𝑥
  • E2𝑥


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

  • A32
  • B6
  • C3
  • D6
  • E23


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

  • A14:
  • B122:
  • C12:
  • D12:
  • E11:


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.

  • A453 m
  • B45 m
  • C603 m
  • D180 m
  • E903 m


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

  • A3𝑥
  • B2𝑥3
  • C2𝑥
  • D𝑥2
  • E3𝑥2


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

  • A3 cm
  • B23 cm
  • C23 cm
  • D1 cm
  • E4 cm


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

  • A3 cm
  • B33 cm
  • C12 cm
  • D23 cm
  • E43 cm


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

  • A34 cm2
  • B33 cm2
  • C3 cm2
  • D32 cm2
  • E1 cm2


In the figure, the length of 𝐴𝐵 is 8.

Find the length of 𝐵𝐶.

  • A4
  • B8
  • C16
  • D2
  • E8

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

  • A2
  • B22
  • C32
  • D2
  • E4

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