Asked by Vincent
Find the area of the triangle. Round to the nearest tenth.
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?
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?
Answers
Answered by
drwls
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.
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.
Answered by
Reiny
In a general triangle ABC
Area = (1/2)(ac)sin B
= (1/2)(12.7)(5.8)sin42.8º
= ....
Area = (1/2)(ac)sin B
= (1/2)(12.7)(5.8)sin42.8º
= ....
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