The length of c is c = 13.3, and the angle measures are A = 17.7 and B = 97.3
<h3>How to determine the missing sides and angles of the triangle?</h3>
From the question, we have the given parameters to be:
b = 10 inches
a = 14 inches
<C = 65 degrees
To calculate the length of c, we use the following equation of law of cosine
c^2 = a^2 + b^2 - 2 * a * b * cos(C)
Substitute the known values in the above equation
c^2 = 14^2 + 10^2 - 2 * 10 * 14 * cos(65 degrees)
Evaluate cos(65 degrees)
c^2 = 14^2 + 10^2 - 2 * 10 * 14 * 0.4226
Evaluate the exponent
c^2 = 196 + 100 - 2 * 10 * 14 * 0.4226
Evaluate the product
c^2 = 196 + 100 - 118.328
Evaluate the sum and the difference
c^2 = 177.672
Take the square root of both sides
c = 13.3
To calculate the angle measure of A, we use the following equation of law of sine
a/sin(A) = c/sin(C)
This gives
14/sin(A) = 13.3/sin(65)
This gives
14/sin(A) = 14.7
Rewrite as:
sin(A) = 14/14.7
Evaluate the quotient
sin(A) = 0.9524
Take the arc sin of both sides
A = 17.7
Lastly, we have
B = 180 - A - C
This gives
B = 180 - 17.7 - 65
Evaluate
B = 97.3
Hence, the length of c is c = 13.3, and the angle measures are A = 17.7 and B = 97.3
Read more about law of cosines and sines at:
brainly.com/question/4372174
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