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A builder leans a five-foot plank of wood against a vertical wall.
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If one end of the plank is three feet from the bottom of the wall, what is the angle between the plank and the wall?
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We have a vertical wall.
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A builder leans a five-foot plank of wood against this wall.
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The end of the plank is three feet from the bottom of the wall.
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What is the angle between the plank and the wall?
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Because we know that the wall is vertical, the angle created here would be a right angle.
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And that means we can use our right angle trig functions to solve this problem.
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We have an unknown angle, the opposite side length, and the hypotenuse.
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If you arenโt sure why this is the hypotenuse, note that the hypotenuse is always the side length opposite the right angle.
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Okay, back to this relationship, the opposite over the hypotenuse is the sin of ๐.
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It is the sine relationship.
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The sine of our missing angle is equal to the opposite side length, three, over the hypotenuse side length of five.
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In order to isolate ๐, we need to take the sine inverse of the sin of ๐.
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And if we take the sine inverse of the left side of the equation, we need to take the sine inverse of the right side of our equation.
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Sine inverse of sin ๐ cancels out and leaves us with our ๐.
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Sine inverse of three over five equals about 36.8699 degrees.
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Just a note, if your calculator told you that the sine inverse was 0.6435 continuing, then your calculator is set to radians.
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And in this problem, weโre trying to solve in degrees.
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Youโll need to change your settings so that your calculator is operating in degrees.
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Now that we know what the angle measure is, we can round it to the nearest hundredth.
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To round to the nearest hundredth, weโll look at the thousandths digit, which is a nine.
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That tells us we round our six up to a seven, and everything to the left of that digits stays the same.
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The angle between the plank and the wall is 36 and 87 hundredths degrees.