How do you use the Pythagorean Theorem to find the missing side of the triangle given: b = 5, c = 8?

1 Answer
Apr 19, 2016

If 8 is the hypotenuse than side a=sqrt(39)

If 8 is not the hypotenuse than sude a=sqrt(89)

Explanation:

You have not declared if the triangle is a right triangle ( has a 90 degree angle) nor have you declared if the side c is the hypotenuse or not. However, by including the use of Pythagoras you have implied it is a right triangle.

Let the unknown side be labeled a

color(blue)("Assumption 1: It is a right triangle and 8 is the hypotenuse")

=>a^2=8^2-5^2" " =" " 64-25" "=" "39

a=sqrt(39)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(blue)("Assumption 2: It is a right triangle and 8 is not the hypotenuse")

->a^2=8^2+5^2 =89

=>a=sqrt(89)