Question

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

Answer 1

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`