a hillside is inclined at an angle of 30 degrees with the horizontal. how much altitude has mary gained after hiking 40 meters up the hill?
x/40 = sin 30°
To calculate the altitude Mary has gained, we can use trigonometry. The angle of inclination of the hillside is given as 30 degrees, and the distance Mary has hiked up the hill is given as 40 meters.
Altitude is the vertical distance from a reference point, in this case, the horizontal ground level. In this context, the altitude is the height gain of Mary up the hill.
We can use the trigonometric function sine (sin) to find the altitude. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite the angle is the altitude, and the hypotenuse is the distance Mary has hiked.
So, let's calculate the altitude gained by Mary:
Step 1: Convert the angle from degrees to radians (since trigonometric functions in most programming languages work with radians instead of degrees).
To convert from degrees to radians, you multiply the angle by (π/180). So, 30 degrees in radians would be:
30 * (π/180)
Step 2: Calculate the altitude using the sine trigonometric function.
altitude = distance * sin(angle)
altitude = 40 * sin(30 * (π/180))
Step 3: Evaluate the expression.
altitude = 40 * sin(0.5236)
altitude ≈ 40 * 0.5
altitude ≈ 20 meters
Therefore, Mary has gained approximately 20 meters in altitude after hiking 40 meters up the 30-degree inclined hillside.