Question

In a right triangle ABC, how do you find b if a=2, c=5 and `C=90^circ`?

Answer 1

`b=sqrt(21)~~4.58`

Explanation:

According to the Pythagorean Theorem in a right triangle with `/_C=90^circ`
`color(white)("XXX")a^2+b^2=c^2`

`color(white)("XXX")rArr b^2=c^2-a^2`

`color(white)("XXX")rArr b=sqrt(c^2-a^2)`

For the given example with `a=2` and `c=5`
this becomes
`color(white)("XXX")b=sqrt(5^2-2^2)=sqrt(25-4)=sqrt(21)`

You could then use a calculator to determine an approximate value for `b`:
`color(white)("XXX")sqrt(21)~~4.582575695`