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Worksheet: The Pythagorean Theorem with 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 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 .

  • A 4 m
  • B m
  • C m
  • D m
  • E m

Q2:

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

Find the length of 𝐡 𝐢 .

  • A2
  • B8
  • C √ 8
  • D4
  • E16

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

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

Q3:

Use the figure to find the value of π‘₯ .

  • A 1 0 √ 3 meters
  • B 1 0 √ 2 meters
  • C 5 √ 3 meters
  • D 5 √ 2 meters
  • E 10 meters

Q4:

Given that 𝐴 𝐡 = 3 , find 𝐡 𝐢 . Give an exact answer.

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

Q5:

Find, in terms of π‘₯ , the length of the hypotenuse of this triangle.

  • A √ 2 π‘₯
  • B 2 √ π‘₯
  • C π‘₯ √ 2
  • D π‘₯ √ 2
  • E 2 π‘₯

Q6:

Find the ratio of the length of 𝐴 𝐡 to the length of 𝐡 𝐢 in its simplest form.

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

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