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 180^o …A + B + C = 180^o

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:

This entry was posted on Monday, September 6th, 2010 at 5:22 am and is filed under 12th Grade, Homework Answers, Math Answers. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.