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

Answer:

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)#