Find the area of the triangle. Round to the nearest tenth.

Question

B= 42.8° a= 12.7 c= 5.8

I found b by using the Pythagorean theorem and got
b= 11.298
but I don't know what to do next after this. I would find the altitude but I don't know angles A and C?

Answer 1

You can only use the Pythagorean theorom with right triangles. This is not one.

The length of side b is given by the law of cosines
b^2 = a^2 + c^2 - 2 ac cos B
= 161.29 + 33.64 - 108.09 = 86.84
b = 9.319

Then use the law of sines to get angles A or C.

b/sin B = a/sin A = c/sin C = 13.716
sin A = a/13.716 = 0.926
A = 112.2 degrees (obtuse)
sin C = 0.423
C = 25.0 degrees

With all that information, you can get the area various ways.

Answer 2

In a general triangle ABC
Area = (1/2)(ac)sin B
= (1/2)(12.7)(5.8)sin42.8º
= ....