I need to calculate the area of the right angle triangle if we know the hypotenuse is 12...... and one of the angles is 60 degrees.

Given the hypotenuse in a right angle triangle is
12

Also, given that one of the angles is 60
degrees.

We need to find the
area.

We will need to determine the length of the
sides.

Let the sides be a , b, and c such that c is the
hypotenuse.

==> A = (1/2) * a *
b

Now we will use cos to find the
sides.

We know that one of the sides =
c*cos60

==> a = 12*cos60 = 12*1/2 =
6

Now we will determine the other side
b.

==> b= 12*sin60 = 12*sqrt3/2 =
6sqrt3

Now we will substitute into the
area.

==> A = (1/2)* a *
b

           = (1/2)*6 * 6sqrt3=
18sqrt3

Then the area of the triangle is A =
18sqrt3 = 31.18 square units.