It's going to be kind of crazy, but you need to use Pythagorean's Theorem for this. That will look like this:
. FOIL out the left side to get
. FOIL out the first of the 2 expressions on the right to get
, and the second of the 2 to get 4x. Our equation now looks like this:
. Combine like terms to get an equation that still has square roots in it that we have to deal with:
and
. We will square both sides to get rid of the square root sign.
. This is a polynomial now that can be factored to solve for x. Bring the 2x over by subtraction and set the polynomial equal to 0.
. Factor out an x, leaving us with x(x-2)=0. That means that x = 0 or x - 2 = 0 and x = 2. Of course if we are solving for the length of a side we know it can't have a side length of 0, so it must have a side length that is a multiple of 2. x = 2
Hello from MrBillDoesMath!
Answer:
4/sin(80)
which is approximately 4.06
Discussion:
From the triangle, not drawn too accurately (see attachment)
sin(80) = side opposite /hypotenuse =>
sin (80) = 4/c => multiply both sides by "c"
c sin(80) = 4/c * c =>
c sin(80) = 4 => divide both sides by sin(80)
c = 4/sin(80)
and 4/sin(80) is approximately 4.06
Thank you,
MrB
This is how I did it, I really hope it helped you with your homework