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For the given figure, find the measure of angle ๐ต๐ด๐ถ, in degrees, to two decimal places.
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The first thing we need to do is identify angle ๐ต๐ด๐ถ, which is here.
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We can call this angle ๐.
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In relation to this angle, we know an opposite side length and the hypotenuse length.
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We know that this is the hypotenuse because itโs the side length thatโs opposite the right angle.
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In right-angle trigonometry, the relationship of opposite over the hypotenuse is sin of ๐.
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We sometimes use the memory device SOHCAHTOA to represent the relationships of sine, cosine, and tangent.
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Sine is the opposite over the hypotenuse.
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That means we can say that sin of ๐ equals eight over 13.
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In order to get ๐ by itself, we need to take the sin 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 the equation.
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The sin inverse of sin of ๐ just equals ๐.
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This angle measure is equal to the sin inverse of eight over 13.
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At this point, weโll need a calculator.
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In a calculator, youโll find the sin inverse of eight over 13.
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Notice that, in my calculator, itโs showing in degrees.
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This is because I know that I want to find the measure of this angle in degrees.
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Once Iโve checked that everything is in degrees, I hit enter and I get ~~37.97987224~~ [37.97987244].
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That means ๐ equals 37.97987244 degrees.
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Weโre rounding to two decimal places.
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Thatโs the hundredths place.
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And so we consider the digit to the right of the hundredths place the deciding digit.
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This deciding digit is larger than five.
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And that means weโll round up.
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The seven in the hundredths place rounds up to an eight.
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And so rounded to two decimal places, ๐ equals 37.98 degrees.
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Now if your calculator gives you something like 0.66, that means itโs operating in radians.
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We can also visually tell that the angle ๐ is larger than half a degree.
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If that happens to you, you need to find in your calculator settings where you change it from degrees to radians.
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And make sure that youโve selected degrees for your function.
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The measure of angle ๐ต๐ด๐ถ equals 37.98 degrees.