In #triangle TUV#, how do you express CosT in terms of t, u, v?

1 Answer
Jan 12, 2017

Answer:

#cosT=(u^2+v^2-t^2)/(2uv)#

Explanation:

the standard cosine rule for triangle with vertices #A,B,C# is:

#a^2=b^2+c^2-2cbcosA#

note the angle in the trig. function is the opposite angle to the side on the LHS

so if we had #CosC# to find the formula would be:

#c^2=a^2+b^2-2abcosC#

so if we have #DeltaTUV# and we want #cosT# we note that we start with the side #t# in the formula

#t^2=u^2+v^2-2uvcosT#

we now rearrange in terms of #cosT#

#2uvcosT=u^2+v^2-t^2#

#cosT=(u^2+v^2-t^2)/(2uv)#