1. Inclination Question

I have a problem in the book asking for inclination with a given slope. I'm told to use formula m = tan(inclination) as long as (0deg < or = Incl < 180deg)

Slope: -6.691

I use tan^-1(-6.691) and get -81.4 but the book says it's 98.5

2. Since the problem said "0deg < or = Incl < 180deg", -81.4 couldn't possibly be the correct answer, could it?

Hint: the tangent function is periodic with period 180 degrees.

3. True

True, it has to be positive. I've tried many different things, like subtracting the angle from 180 first. I'm stuck.

4. Did you get 180-81.4= 98.6 rather than 98.5? It's round off error. The "principal value" of $tan^{-1}(-6.691)$ is -81.4998 to 4 significant figures which rounds off to -81.5, not -81.6.

5. Now i see

I now see that you're subtracting the angle from 180 afterwards. But really it's addition, since -81.4 is negative. So, if the slope is negative, the angle will be negative. Add it to 180 to get the inclination. Is this correct?

6. Yes, -81.5+ 180= 180- 81.5. "subtract 81.5" is exactly the same thing as "add -81.5".