Question

In triangle abc, cos A= -0.6. Find A and Tan A

Answer 1

Part 1)
`A=126.87^o`

Part 2)
`tan(A)=-(4)/(3)`

Explanation:

we have

`cos(A)=-0.6`

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

`cos(A)=-0.6`

using a calculator

`A=cos^(-1)(-0.6)=126.87^o`

step 2

Find the sin(A)

we know that

`sin^2(A)+cos^2(A)=1`

substitute the value of cos(A)

`sin^2(A)+(-0.6)^2=1`

`sin^2(A)=1-0.36`

`sin^2(A)=0.64`

`sin(A)=0.8`

step 3

Find tan(A)

we know that

`tan(A)=(sin(A))/(cos(A))`

substitute the values

`tan(A)=(0.8)/(-0.6)`

Simplify

`tan(A)=-(4)/(3)`