Answer:
Part 1) [tex]A=126.87^o[/tex]
Part 2) [tex]tan(A)=-\frac{4}{3}[/tex]
Step-by-step explanation:
we have
[tex]cos(A)=-0.6[/tex]
The cos(A) is negative, that means that the angle A in the triangle ABC is an obtuse angle and the value of the sin(A) is positive
The angle A lie on the II Quadrant
step 1
Find the measure of angle A
[tex]cos(A)=-0.6[/tex]
using a calculator
[tex]A=cos^{-1}(-0.6)=126.87^o[/tex]
step 2
Find the sin(A)
we know that
[tex]sin^2(A)+cos^2(A)=1[/tex]
substitute the value of cos(A)
[tex]sin^2(A)+(-0.6)^2=1[/tex]
[tex]sin^2(A)=1-0.36[/tex]
[tex]sin^2(A)=0.64[/tex]
[tex]sin(A)=0.8[/tex]
step 3
Find tan(A)
we know that
[tex]tan(A)=\frac{sin(A)}{cos(A)}[/tex]
substitute the values
[tex]tan(A)=\frac{0.8}{-0.6}[/tex]
Simplify
[tex]tan(A)=-\frac{4}{3}[/tex]
