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

Adjacent side= 35,

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

Adjacent² = 3600

Adjacent side= 60

For third column:

Opposite side = 1

Adjacent 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

Adjacent² = 3

Adjacent side= √3

For fifth column:

Adjacent side= 1

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

Adjacent side= 20

By Pythagoras Theorem

Hypotenuse² = Opposite side² + Adjacent²

= 21² + 20²

Hypotenuse² = 841

Hypotenuse = 29

For seventh column:

Opposite side = 8

Adjacent side= 15

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

Adjacent² = 16

Adjacent side= 4

For ninth column:

Opposite side = 1

Adjacent side= 2√2

By Pythagoras Theorem

Hypotenuse² = Opposite side² + Adjacent²

= 1² + (2√2)²

Hypotenuse² = 9

Hypotenuse = 3