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Ontario MTH1W · Geometry and Measurement · E1.5

Right triangles and composite shapes

Use the Pythagorean relationship and shape decomposition to solve measurement problems.

The core idea

For a right triangle, a² + b² = c², where c is the hypotenuse opposite the right angle. In a composite shape, split the figure into familiar pieces before calculating.

Learning example

Find a ladder length

A ladder reaches 8 m up a wall and its base is 6 m from the wall. How long is the ladder?

  1. 1

    The ladder is the hypotenuse: c² = 6² + 8².

  2. 2

    c² = 36 + 64 = 100.

  3. 3

    Take the positive square root: c = 10.

AnswerThe ladder is 10 m long.

A common mistake

Using 8 as the hypotenuse because it is the taller drawn side. The hypotenuse is defined by its position opposite the right angle.

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