ANSWER:
The value of angle A is 80.61°
STEP-BY-STEP EXPLANATION:
Given:
a=26.61 km,
b= 21.46 km
c= 19.62 km
We can calculate the value of angle A by means of the law of cosines, which is as follows:
[tex]a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos(A)[/tex]We solve for A and then substitute to calculate it, like this:
[tex]\begin{gathered} 2\cdot b\cdot c\cdot\cos(A)=b^2+c^2-a^2 \\ \\ \cos(A)=\frac{b^2+c^2-a^2}{2\cdot b\cdot c} \\ \\ A=\cos^{-1}\left(\:\frac{b^2+c^2-a^2}{2\cdot\:b\cdot\:c}\:\right) \\ \\ \text{ We repalcing} \\ \\ A=\cos^{-1}\left(\:\frac{21.46^2+19.62^2-26.61^2}{2\cdot\:21.46\cdot\:19.62}\:\right) \\ \\ A=\cos^{-1}(0.1631) \\ \\ A=80.61\degree \end{gathered}[/tex]The value of angle A is 80.61°
