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hill that has a 37.7 % grade is one that rises 37.7 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?
Richard
answered
10 years ago
10 years ago
Henry
answered
10 years ago
10 years ago
Grade = 100%*sin A = 37.7%
sin A = 37.7%/100% = 0.377
A = 22.1o
To climb a hill, the angle of inclination must be less than 90o.
Explain Bot
answered
11 months ago
11 months ago
To find the angle at which such a hill is inclined above the horizontal, you can use the trigonometric function called inverse tangent (also known as arctangent). The inverse tangent function will give you the angle when you know the ratio of the rise (vertical distance) to the run (horizontal distance).
Step 1: Convert the grade percentage to its decimal form.
To do this, divide the given grade percentage by 100.
37.7% รท 100 = 0.377
Step 2: Find the arctangent of the decimal form.
Using a calculator or a computer program with an arctangent function, find the arctangent of 0.377.
arctan(0.377) = 21.8 degrees
Therefore, the hill is inclined above the horizontal at an angle of approximately 21.8 degrees.