Question

Solve for the angles of the triangle described below. Express all angles in degrees and round to the nearest hundredth.a = 6, b = 6,C = 8l

Answer 1

ANSWER:

A = 48.19°

B = 48.19°

C = 83.62°

STEP-BY-STEP EXPLANATION:

Given:

a = 6, b = 6, c = 8

We can calculate the angles by means of the law of cosines, just like this:

$A=\cos^{-1}\left(\frac{b^2+c^2-a^2}{2bc}\right)$

We apply in each case to calculate the 3 angles, as follows:

$\begin{gathered} A=\cos^{-1}\left(\frac{6^2+8^2-6^2}{2\left(6\right)\left(8\right)}\right)=\cos^{-1}\left(\frac{2}{3}\right) \\ \\ A=48.19^{\circ\:} \\ \\ B=\cos^{-1}\left(\frac{6^2+8^2-6^2}{2\left(6\right)\left(8\right)}\right)=\cos^{-1}\left(\frac{2}{3}\right) \\ \\ B=48.19^{\operatorname{\circ}} \\ \\ C=\cos^{-1}\left(\frac{6^2+6^2-8^2}{2\left(6\right)\left(6\right)}\right)=\cos^{-1}\left(\frac{1}{9}\right) \\ \\ C=83.62^{\circ\:} \end{gathered}$

Therefore, the angles are the following:

A = 48.19°

B = 48.19°

C = 83.62°