Question

Some mountains in the Alps are very steep and have a grade of 42.7%. To the nearest degree, what
angle do these mountains make with a horizontal line?

Answer 1

by grade you mean gradient ?

Answer 2

yes

Answer 3

\[\large slope=\tan \theta \]

\[\large \tan^{-1} (slope)= \theta \]

Answer 4

so is the answer 23 degrees

Answer 5

A "percent grade" means that for every 100 units distance out, you drop the given number of units down, so in your example, you would have a triangle formed by the horizontal line 100 units long going straight out from your starting point and then another line dropping 42.7 units straight down. Sooo, you can use a trigonometry rule to solve for the desired angle -- sine(x) = opposite / adjacent = 42.7/100 = 0.4270... so inverse sine of that is approximately 25.28 degrees.

Answer 6

i+i credit