A mound is raised 8 inches at its highest point, and sloped down so that it meets the flat ground at a 12° angle.?
Steven is building a pitcher’s mound in his backyard so he is ready for baseball season. The mound is built like a small dirt “hill.” The league requires it is raised 8 inches at its highest point, and then sloped down so that it meets the flat ground at a 12° angle. How long will the front of the pitcher’s mound need to be?
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I am assuming the question is asking for the slant distance from the top of the mound to base of the mound.
let the slant distance = y
====> sine of an angle = opposite side divided by the hypotenuse side
angle = 12°
opposite = 8”
hypotenuse = y
sin12° = 8/y
y = 8/sin12°
y = 38.48”
━━━━━
Otherwise if the question is asking for the horizontal distance, here is the procedure.
let horizontal distance = x
====> tangent of an angle = opposite side divided by the adjacent side
angle = 12°
opposite = 8”
adjacent = x
tan12° = 8/x
x = 8/tan12°
x = 37.64”
━━━━━
8/x = tan(12)
x = 8/tan(12)
= 37.63704088
= 37.64 in