What is the approximate measure of angle T in the triangle below?
Accepted Solution
A:
Answer:[tex]T=79\degree[/tex]Step-by-step explanation:Recall and use the cosine rule to find the approximate value of angle T.[tex]|SU|^2=|ST|^2+|TU|^2-2(|ST|)(|TU|)\cos T[/tex]We plug in the values of the side lengths to obtain;[tex]4.3^2=3.9^2+2.7^2-2(3.9)(2.7)\cos T[/tex][tex]18.49=15.21+7.29-21.06\cos T[/tex][tex]18.49=22.5-21.06\cos T[/tex][tex]18.49-22.5=-21.06\cos T[/tex][tex]-4.01=-21.06\cos T[/tex][tex]4.01=21.06\cos T[/tex][tex]\frac{4.01}{21.06}=\cos T[/tex][tex]0.1904=\cos T[/tex][tex]T=\cos^{-1}(0.1904)[/tex][tex]T=79.02[/tex]Angle T is approximately 79 degrees.