# In the following table, a ratio is given in each column. Find the remaining two ratios in the column and complete the table.  For first column: cosθ = 35/37

Hypotenuse = 37

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

Opposite side2 = Hypotenuse2 - Adjacent2

= 372 - 352

= 1369 – 1225

Opposite side2 = 144

Opposite side = 12

For second column: Opposite side = 11

Hypotenuse = 61

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

Adjacent2 = Hypotenuse2 - Opposite side2

= 612 - 112

= 3721 – 121

For third column: Opposite side = 1

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

= 1 + 1

Hypotenuse2 = 2

Hypotenuse = √2

For fourth column: Opposite side = 1

Hypotenuse = 2

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

Adjacent2 = Hypotenuse2 - Opposite side2

= 22 - 12

= 4 – 1

For fifth column: Hypotenuse = √3

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

Opposite side2 = Hypotenuse2 - Adjacent2

= (√3)2 - 12

= 3 – 1

Opposite side2 = 2

Opposite side = √2

For sixth column: Opposite side = 21

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

= 212 + 202

Hypotenuse2 = 841

Hypotenuse = 29

For seventh column: Opposite side = 8

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

= 82 + 152

Hypotenuse2 = 289

Hypotenuse = 17

For eighth column: Opposite side = 3

Hypotenuse = 5

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

Adjacent2 = Hypotenuse2 - Opposite side2

= 52 - 32

= 25 – 9

For ninth column: Opposite side = 1

By Pythagoras Theorem

Hypotenuse2 = Opposite side2 + Adjacent2

= 12 + (2√2)2

Hypotenuse2 = 9

Hypotenuse = 3

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