What is the approximate measure of angle T in the triangle below?

Question

asked Feb 2, 2020 200k views

2 Answers

Muhammad Naderi · Answer 1 · 2020-02-08T18:44:01+0000

Answer:

$T=79\degree$

Explanation:

Recall and use the cosine rule to find the approximate value of angle T.

$|SU|^2=|ST|^2+|TU|^2-2(|ST|)(|TU|)\cos T$

We plug in the values of the side lengths to obtain;

$4.3^2=3.9^2+2.7^2-2(3.9)(2.7)\cos T$

$18.49=15.21+7.29-21.06\cos T$

$18.49=22.5-21.06\cos T$

$18.49-22.5=-21.06\cos T$

$-4.01=-21.06\cos T$

$4.01=21.06\cos T$

$(4.01)/(21.06)=\cos T$

$0.1904=\cos T$

$T=\cos^(-1)(0.1904)$

T=79.02

Angle T is approximately 79 degrees.