How do you find the exact value of the third side given #triangle ABC#, #a=62.5, b=44.7, mangleC=133#?

1 Answer
Apr 17, 2017

Answer:

Third side #c=98.565#

Explanation:

We can use the cosine formula to find the length of a side or size of an angle. For a triangle with sides #a,b# and #c# and angles #A, B# and #C# the cosine rule can be written as #c^2=a^2+b^2-2abcosA#.

Here #a=62.5#, #b=44.7# and #m/_C=133°#, hence

#c^2=62.5^2+44.7^2-2×62.5×44.7×cos133°#

= #3906.25+1998.09-125×44.7×(-0.682)#

= #3906.25+1998.09+3810.675#

= #9715.015#

Hence #c=sqrt9715.015=98.565#