The common formula used to calculate the area of a triangle is:
S = 1/2 AC x BH
where AC is the base of the triangle and BH is it's height.
Let's say 78.5ft side is the base side (AC). All we have to do now is to calculate the height.
Heights always make up a right angle with the side they root upon (the base side in our case). It means we must position H on the AC side so that AHB makes up a right angle. BH is the height we seek.
ABH is a right triangle with AB as it's hypotenuse. BH is the opposite cathetus to the BAH angle (which is gven - 38 degrees). The formula that links an angle of a right triangle with it's opposite cathetus and the hypotenuse is this:
sin a = opp.cath. / hypotenuse
or in our case:
sin (BAH) = BH / AB
Since AH is the height we're looking for, let's transform the formula into this:
BH = sin (BAH) x AB
BH = sin 38deg x 39.5 = 0.61566148 x 39.5 ~ 24.32 feet
Make sure your calculator interprets 38 as degrees when calculating the sine.
S = 1/2 AC x BH = 1/2 x 78.5 x 24.32 = 954.56 ft2
which is roughly answer#1
