Speaker Woofer Enclosure
22
Dec/100
Dec/100
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Math Circles Question (Trigonometry)?
A round, 12-inch woofer is mounted to the bottom of a rectangle speaker enclosure with an inner width measurement of 12 inches how far is the Bottom right corner of this box to the Center of the circle of the woofer? Round your answer to the nearest 2 decimal places
There's a triangle formed by the center of the woofer (lets call it C), the point at the bottom of the box directly below the center point (call it B), and the point at the corner (A). We can easily figure out that the length of line CB is 6 inches (1/2 of the 12 inch woofer), and BA likewise has to be 6 inches.
So we can either figure out the length of CA using the Pythagorean equation,
"a^2 + b^2 = c^2"
6^2 + 6^2 = c^2
72 = c^2
c = sqrt(72) = 8.49 inches,
but since this is trigonometry, we'll instead use the rule
"sine(a) = opposite / hypotenuse":
sine(45) = 6 / c
0.7071 = 6 / c
c = 6 / 0.7071 = 8.49 inches.
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