# One Trigonometry Question

1. Oct 16, 2011

### Zhuhaolin

Hi, I'm here to just ask a simple question: What is "grade" in Trig?

I have been presented the question: "A bus traveled up a road that had a grade of 15%. What angle does this correspond to, what ratio and what slope is this?"

I have not made an attempt on this question because I don't know what "grade" here means.

2. Oct 16, 2011

### phyzguy

The 'grade' of a road refers to the slope. The grade is equal to the vertical distance traveled divided by the horizontal distance traveled. So if the grade is 15%, the angle between the road and the horizontal will be arctan(0.15) which is approximately 8.5 degrees.

3. Oct 19, 2011

### Maritime123

Like phyzguy said, it's just the slope. It's good to know that there are a number of terms used for slope. Like grade, gradient, rise, pitch, ect..

4. Oct 21, 2011

### zgozvrm

5. Oct 21, 2011

### Staff: Mentor

No, not at all. The context of the question indicates that the bus is going up a hill whose slope or gradient is 15/100 or 0.15.

Not coincidentally, the tangent of the angle the road makes with the horizontal is also 0.15.

Last edited: Oct 21, 2011
6. Oct 22, 2011

### zgozvrm

Sorry. Somehow, I didn't see the part about the bus. I was sure that didn't show up when I read it yesterday - I was really tired though!

7. Oct 23, 2011

### dynamicsolo

Well, I learned something interesting out of this. The gradian was introduced along with the rest of the metric system after the French Revolution, but it only caught on in a few countries and in certain fields like civil engineering and surveying (so there it is in your calculator modes). Basically, it's there to "decimalize" the right angle. (Interestingly, all attempts to expunge the sexagesimal system from timekeeping, cartography and navigation, and angle measurement generally, have been failures. Dang those persistent Sumerians!)

As for the grade of an incline, it is just a convenient way to turn the tangent value of the incline from a fraction into a percentage (as commented on above). One useful application of it is that an object will slide down the incline (static friction fails) when the tangent value (or the grade) exceeds the coefficient of static friction between the surfaces of the object and the incline.

Last edited: Oct 23, 2011