1 Answer

Purring Pigeon · Answer 1 · 2023-01-27T11:22:23+0000

The triangle has sides

a=8

b=14

c=19

You need to determine the measure of x

To determine the value of x you have to use the Law of Cosines that states that:

$a^2+b^2-ab\cos \theta=c^2$

Where a, b, and c are the sides of the triangle, and theta represents the angle we are looking for.

So first step is to replace the formula with the given data and solve the exponents

$\begin{gathered} 8^2+14^2-8\cdot14\cos thetha=19^2 \\ 64+196-112\cos \theta=361 \\ 260-112\cos \theta=361 \end{gathered}$

Next solve for the cosine of theta:

$\begin{gathered} -112\cos \theta=361-260 \\ -112\cos \theta=101 \\ \cos \theta=(101)/(-112) \\ \cos \theta=-(101)/(112) \end{gathered}$

And calculate the inverse cosine to determine the measure of the angle

$\begin{gathered} \theta=\cos ^(-1)(-(101)/(112)) \\ \theta=154.39 \end{gathered}$

Your comment on this question: