Question

I need serious help on this!! Please!!
The Colorado river drops from 3200 feet at Lake Mead to 900 feet elevation at Lee's Ferry, a river distance of 270 miles. What is the gradient in degrees?

Answer 1

Hello, Yana,
On the surface this appears to be a routine slope = rise / run problem. You get into your kayak at Lake Mead, 3200 feet above sea level, travel 270 miles down the river, and end up at Lee's Ferry, 900 feet above sea level. What's the "rise?" the "run?" what's the "slope?"

Actually, the problem's not that simple, since the Colorado River doesn't flow along a nice, straight path for 270 miles. It zigs and zags. We could either assume that the river runs straight (which is never going to happen!), or we could assume that the actual distance along the river is actually greater, but that we think of 270 miles as "as the crow flies."

Suppose you find the "slope" in the usual fashion: slope = rise / run. It'll be negative, since the river is descending. If you've found your slope in this manner, then you've also found your "gradient." See www.mathsisfun.com/gradient.html for a reference.

Answer 2

Thanx!:) The only part that I need help with is setting up the equation. I have it, but I don't know if it's right though..

Answer 3

Given that there's some ambiguity about this problem (e. g., straight river, crooked river, actual distance down the river, "as the crow flies" distance down the river, and so on, we may have to make assumptions and then proceed accordingly In your shoes, I'd write my assumptions to include with my work towards finding that "gradient."

Answer 4

Ok. Here's what I have:
\[2700ft x \frac{ 1 }{ 5280 } = 0.511\]
Is that correct?

Answer 5

Here we have two sides of a triangle and need an angle. The river distance is the hypotenuse and the vertical drop is the opposite angle. However, there is a catch. The measurements are not in the same units, and they must be to use our trigonometric formulas. So first, we'll convert the drop to miles (we could have converted the distance to feet - it doesn't matter.)
2700ft*(1mi/5280ft)= 0.511mi

Now we can use the formula for sine to calculate the angle x
sin=opp/hyp
substituting in,
sin(x)=0.511mi/270mi
so
sin(x)= 0.00189
to solve for x, the angle, take the inverse sine of each
sin-1(sin(x))= sin-1(0.00189)
since sin-1(sin(x))=x , our result is.......?

Answer 6

I got 0.11 degrees..

Answer 7

thats correct