Solve the Triangle. Round Angle Measures to the Nearest Minute & Side Measures to the Nearest Tenth. a=11.4, b=13.7, c=12.2
Solution:
These are the formulas used to solve triangles:
1. The sum of the internal angles equals 180o …A + B + C = 180o
2. The ‘sine rule’ …
3. The ‘cosine rule’ …
a² = b² + c² – 2bc cosA
or
b² = a² + c² – 2ac cosB
or
c² = b² + a² – 2ba cosC
In the problem that you gave us, we know the length of the three sides of the triangle:
a = 11.4
b = 13.7
c = 12.2
When no angles are known, the cosine rule is the only option, so 11.42 =13.72 +12.22 – 2*13.7*12.2*cosA….Therefore cosA = 0.617955.
You can now use a calculator or a table to find the value of A. You should get A = 0.9047 radians = 51.833 degrees = 51 degrees and 50 minutes.
Use the sine rule to find one of the remaining angles.
=
So sin(B) = = 0.944835
You can now use a calculator or a table to find the value of B. You should get B = 1.237 radians = 70.8801 degrees = 70 degrees and 53 minutes.
Finding the third angle is easy, since we know that A + B +C =180 degrees. C = 180 – 51.833 – 70.880 = 57.287 degrees = 57 degrees and 17 minutes.
Visual representation:
Posted in 12th Grade, Homework Answers, Math Answers.
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