Answer
a) 40
b) $ 40\sqrt3$
c) $40\sqrt{2}$
Work Step by Step
In each case, we must find the height to find the area.
a) We know this forms a 30-60-90 triangle, so the height it:
$h = 1/2(10) = 5$
$ A = (b)(h) = (8)(5) = 40$
b) We know this is a 30-60-90 triangle, but this time A is the 60 degree angle. Thus:
$ h = 10 \times \frac{\sqrt3}{2}= 5\sqrt3$
$ A = (b)(h) = (5\sqrt3)(8) = 40\sqrt3$
c) The third triangle formed is a 45-45-90 triangle. Thus:
$h = 10 \times \frac{\sqrt{2}}{2} = 5 \sqrt2$
$A = (5\sqrt{2})(8) = 40\sqrt{2}$
