Two corners of an isosceles triangle are at #(9 ,6 )# and #(7 ,2 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?
1 Answer
Explanation:
let
We are given that the
Let "a" and "c" be the other two sides.
For a triangle,
Substituting in the values for "b" and the Area:
Solve for the height:
Let
We can find the length of side "a", using the following equation:
Substitute in the values for "h" and "C":
Intuition tells me that side "c" is the same length as side "a" but we can prove this using the Law of Cosines:
Substitute in the values for a, b, and C: