Expert: Paul Klarreich - 11/7/2006

Question
Hello
I am having some trouble with the following question:

Find the area of each triangle.  Use a different area formula for each triangle.  The triangle that i presently have have the measures: a=9, b= 12, c= 14, Angle A = 39.4, angle B = 58.2, angle c = 82.4.

The area formulas i know are from the Law of Sines and Hero's law.

Please help me.

Answer
Questioner:  Ajay
Category:  Calculus
 
Subject:  Area of triangles
Question:  Hello
I am having some trouble with the following question:

Find the area of each triangle.  Use a different area formula for each triangle.  The triangle that I presently have have the measures: a=9, b= 12, c= 14, Angle A = 39.4, angle B = 58.2, angle C = 82.4.

The area formulas I know are from the Law of Sines and Hero's law.
......................................
Hi, Ajay,

If you have that much information, it shouldn't be too hard to get the area.  Since you DON'T want to use Hero's formula, how about this one:

Area = 1/2 ab sin C.

You can probably try it with all the combinations of a,b,C, then  b,c,A, then a,c,B.   It should work out about the same for all three.

Like this (using my Windows calculator)

Area = 1/2 ( 9)(12) sin 82.4 = 53.525639173583252998544855553643

Area = 1/2 (12)(14) sin 39.4 = 53.317363108990478812372873336953

Area = 1/2 ( 9)(14) sin 58.2 = 53.543239658172427323289938673699

Not bad.