Using the Pythagorean Relationship, Homework Book

1. RED is the answer
The Pythagorean relationship can be used to determine the Length of the Hypotenuse of a right triangle when the lengths of the two Legs are known.

3. Question - Determine the length of each hypotenuse. Show your work.
a)
a squared + b squared = c squared
40cm squared + 9cm squared = c squared
(40x40) + (9x9) = c squared
1600cm + 81cm = c squared
The square root of 1681cm = c squared
41 cm squared = c squared


b)
a squared + b squared = c squared
12m squared + 35m squared = c squared

(12x12) + (35x35) = c squared

144m squared + 1225m squared = c squared
The square root of 1369m squared = c squared

37m squared = c squared

5. Question - Calculate the missing side length for each right triangle, to the nearest tenth of a centimetre. Show your work.

a)
a squared = c squared - b squared
a squared = 6 cm squared - 5 cm squared
a squared = (6x6) - (5x5)
a squared = 36cm squared - 25cm squared
The square root of 11 = a squared
a squared = 3.31cm squared

b)

a squared = b squared - c squared
a squared = 7cm squared - 12cm squared
a squared = (7x7) - (12x12)
a squared = 49cm squared - 144cm squared
The square root of 95 = a squared
a squared = 9.74

7. Question - A triangle is made up of two smaller congruent right triangles.

a)

a squared + b squared = c squared

4m squared + 2m squared = c squared

(4x4) + (2x2) = c squared

16+ 4 = c squared

The square root of 20 = c squared
4.5 = c squared

b)

a squared = c squared - b squared

a squared = 8m squared - 4.5 squared

a squared = 8m squared + 4.5m squared + 4.5m squared

a squared = 17m squared

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