Question

How do you solve the right triangle ABC given a=2, c=7?

Answer 1

`b=3sqrt(5)` (assuming the side with length `c` is the hypotenuse)

Explanation:

If `c` is the hypotenuse then
`color(white)("XXX")c^2=a^2+b^2`
or
`color(white)("XXX")b^2=c^2-a^2`

for the given values of `a` and `c`
`color(white)("XXX")b^2=7^2-2^2=49-4=45`
which implies
`color(white)("XXX")b=sqrt(45)=sqrt(3^2 * 5) = 3sqrt(5)`

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If the side with length `b` is the hypotenuse then
(using logic similar to the above)
`color(white)("XXX")b==sqrt(53)`