Work out the lengths of sides a and b.

Give your answers to 1 decimal place.

17 cm

8 cm

12 cm

1

5 cm

Pythagoras' Theorem -

Answer:

[tex]a = 9.4[/tex]

[tex]b = 12.0[/tex]

Step-by-step explanation:

Given

See attachment

Required

Determine the values of a and b

To solve for a, we consider the first triangle.

Using Pythagoras:

[tex]a^2 = 8^2 + 5^2[/tex]

[tex]a^2 = 64 + 25[/tex]

[tex]a^2 = 89[/tex]

Take square root of both sides

[tex]a = \sqrt{89[/tex]

[tex]a = 9.4[/tex] -- approximated

To solve for b, we consider the second triangle.

Using Pythagoras:

[tex]17^2 = 12^2 + b^2[/tex]

[tex]289 = 144 + b^2[/tex]

Collect Like Terms

[tex]b^2 = 289 - 144[/tex]

[tex]b^2 = 145[/tex]

Take square root of both sides

[tex]b = \sqrt{145[/tex]

[tex]b = 12.0[/tex] --- approximated

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