Question

Two corners of an isosceles triangle are at `(8 ,2 )` and `(4 ,7 )`. If the triangle's area is `9`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three angles are (2.8111, 4.2606, 4.2606)

Explanation:

Length `a = sqrt((8-4)^2 + (2-7)^2) = sqrt 41 = 6.4031`

Area of `Delta = 64`
`:. h = (Area) / (a/2) = 9 / (6.4031/2) = 9 / 3.2016 = 2.8111`
`side b = sqrt((a/2)^2 + h^2) = sqrt((3.2016)^2 + (2.8111)^2)`
`b = 4.2606`

Since the triangle is isosceles, third side is also `= b = 4.2606`

Measure of the three sides are (2.8111, 4.2606, 4.2606)