find m∠r. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠r = °

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines for finding an angle in a triangle with sides (a), (b), (c) is (\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}). In (\triangle TRS), let (a = 6), (b=13), (c = 16), and we want to find (\angle R). So (\cos R=\frac{6^{2}+13^{2}-16^{2}}{2\times6\times13}).

Step2: Calculate the numerator

[ \begin{align*} 6^{2}+13^{2}-16^{2}&=36 + 169-256\ &=205 - 256\ &=- 51 \end{align*} ]

Step3: Calculate the denominator

(2\times6\times13=156)

Step4: Find the cosine - value of (\angle R)

(\cos R=\frac{-51}{156}\approx - 0.327)

Step5: Find the measure of (\angle R)

(R=\cos^{-1}(-0.327)\approx109.1^{\circ})

Answer:

(109.1)