Question

How do i find k?

Answer 1

`10sqrt2` mi

Explanation:

A 45-45-90 degrees triangle, has three side rules:
Side opposite to 90 degrees: `xsqrt2`
Side opposite to 45 degrees: `x`
Side opposite to 45 degrees: `x`

And since the hypotenuse, or the side opposite to 90 degrees is 20:
`xsqrt2=20`
`x=20/sqrt2*sqrt2/sqrt2= (20sqrt2)/2= 10sqrt2`

Answer 2

`k=10sqrt2`

Explanation:

`"since the triangle is right use "color(blue)"trig ratio"`

`"there are 2 possible approaches here"`

`•color(white)(x)cos45^@="adjacent"/"hypotenuse"=k/20`

`rArrk=20xxcos45^@=20xx1/sqrt2=(20sqrt2)/2=10sqrt2`

`color(red)"OR"`

`•color(white)(x)sin45^@="opposite"/"hypotenuse"=k/20`

`rArrk=20sin45^@=20xx1/sqrt2=10sqrt2`