how do you find the grade of a mountain using trigonometry?

Answer 1

I take it that you want what Americans call the grade (of the mountain's slope) and we British call the GRADIENT.

The gradient of a road or mountain is defined as the RISE (that is, the vertical height difference between two points P and Q on the road or mountainside) divided by the distance travelled between those two points ON the road or mountainside.

In other words, the "grade" or "gradient" is the SINE of the angle that the road or mountain path makes with the horizontal. It is normally expressed as a grade (or gradient) of

"1 in D"

where for example for every increase in elevation by one unit (feet, metres, etc.), you travel a distance of D in those same units. (The sine of the angle of elevation is thus 1/D.)

Live long and prosper.

Answer 2

Grade, at least when referring to roads, is the change in elevation divided by the distance, and expressed as a percent. This would be sinθ expressed in percent. For example, an 11% grade, which is considered quite steep, is an angle of sin^-1(0.11), or about 6°. A 45° slope would be a 70% grade.

Answer 3

Draw a right angled triangle ABC.
Vertical height , h , = AB
Horizontal = BC , a known measured distance.
Angle of elevation to top of mountain from C = θ ,a known measured angle.
tan θ = h / BC
h = BC tan θ
Height can then be calculated.

Answer 4

in case you prefer to work out how severe a brilliant tree is, you ought to use trig. in case you prefer to construct a deck on your place (like I did). in case you prefer to degree the attitude of your driveway. in case you prefer to work out how extensive a river is. Get the photograph?