Expert: Sherman D. - 3/8/2005

Question
1) in triangle ABC, a=12, b=15, and angle C = 65 degrees. find the area of triangle ABC to 3 significant figures.

Answer
Since the work i have tried doesn't come out right, all i can say is to go to http://mathforum.org/dr.math/faq/formulas/faq.triangle.html

with the info you have given me, this problem sounds more like a Scalene triangle. Which a right triangle can also be scalene or isosceles.

for ex:
Isosceles
90°, 45°, 45°
Scalene
90°, 65°, 25°

So your problem, having a 65° angle, would be a scalene right triangle, since no 2 angles are the same.

I think you would still use the Area for a right triangle.

If your problem truly is a right triangle and not a scalene triangle, then

a = 12 would have to be the length of one side
b = 15 would have to be the hypothenuse
c would have to be the other side

When you use
a^2 + c^2 = b^2
12^2 + c^2 = 15^2
144 + c^2 = 225
c^2 = 81
c = 9

However, since angle "C" is 65° and angle "A" would have to be 25°, this means that side "c" would have to be in between side "a" and "b", which in this case side "c" is less than side "a" and "b", so to me this seems wrong somewhere.

anyway, i got the answer to be 54.0 whether the info you have provided me is correct or not.

Side "c" would have to be 12 and side "a" would have to be 9.

If angle "A" were 65°, then side "c" would be correct.