Question

if he distance from the town of Bree to weathertop is 8 miles on a 45 degree upward slope, what is the elevation gain (omit units)?

Answer 1

8*sin45=5.6568 think of it as a triangle

Answer 2

The elevation gain is 4√2 or 5.6569

Explanation:

Consider the provided information.

The distance from the town of Bree to weathertop is 8 miles on a 45 degree upward slope,

The required figure is shown in figure 1.

Here, the triangle is right angle triangle with one angle 45 degree.

Thus, the measure of angles will be: 90°, 45° and 45°

Therefore, both legs of the triangle must be equal. Now by using Pythagorean Theorem,

`x^2+x^2=8^2\\2x^2=64\\x^2=32\\x= √(32) \\x= 4√(2)\ or\ 5.6569 (approximately)`

Hence, the elevation gain is 4√2 or 5.6569