Question

In a right angle the hypotenuse is Xcm Adjacent is y cm while the opposite is Z cm , the length of the hypotenuse is X cm , is given by the formula X=√x^2+y^2

a) Find the value of x when y = 2 1/2 and z = 6cm
b) Find the value of y when X = 16 and X^2 = 60

Answer 1

It appears that there may be a typo in the original question, as if:

• y is the adjacent
• z is the opposite
• X is the hypotenuse

of a right triangle, then using Pythagoras' Theorem:

`y^2+z^2=X^2`

`\implies X=√(y^2+z^2)`

a) Given:

• 
  `y=2 \frac12=2.5`
• 
  `z=6`

And using
`X=√(y^2+z^2)` :

`\implies X=√(2.5^2+6^2)`

`\implies X=√(42.25)`

`\implies X=(13)/(2)`

b) Given:

• 
  `X=16`
• 
  `z^2=60`

And using
`X=√(y^2+z^2)` :

`\implies 16=√(y^2+60)`

`\implies 256=y^2+60`

`\implies 196=y^2`

`\implies y=14`