Angle A = 36.87°.
Solution:
Given data:
The side opposite to angle A is a.
The side opposite to angle B is b.
The side opposite to angle C is c.
a = 6, b = 8, c = 10
Using law of cosine:
[tex]a^{2}=b^{2}+c^{2}-2 b c \cos A[/tex]
Substitute the given values in the formula,
[tex]6^{2}=8^{2}+10^{2}-2\times 8 \times 10 \cos A[/tex]
[tex]36=64+100-160 \cos A[/tex]
[tex]36=164-160 \cos A[/tex]
Subtract 164 from both sides of the equation.
[tex]-128=-160 \cos A[/tex]
Divide by –160 on both sides of the equation.
[tex]$\frac{-128}{-160} =\frac{-160 }{-160 } \cos A[/tex]
[tex]$\frac{4}{5} =\cos A[/tex]
Switch the sides.
[tex]$\cos A=\frac{4}{5}[/tex]
[tex]$ A=\cos^{-1}\left(\frac{4}{5}\right)[/tex]
A = 36.87°
Hence angle A = 36.87°.
