WEBVTT
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Find the value of 𝜃, giving the answer in radians to two decimal places.
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The first thing we wanna notice is that this triangle sits inside a rectangle.
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And that confirms for us that this angle on the bottom is a right angle.
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Once we know that, we can use our trig ratios to find the angle measure that’s missing.
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If angle 𝜃 is our reference point, the side measuring 16 centimeters is the opposite side and the side measuring 20 centimeters is the hypotenuse.
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Opposite over hypotenuse is the sine ratio.
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In our triangle, sine of 𝜃 equals 16 over 20.
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But how do we isolate this angle measure?
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We take the sine inverse.
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The sine inverse of sine 𝜃 is equal to 𝜃.
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And if we take the sine inverse on the left side of our equation, we have to take the sine inverse on the right side of our equation.
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Our angle measure 𝜃 is equal to the sine inverse of 16 over 20.
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Now you’ll use some form of technology: a calculator, a computer, or maybe even a chart with listed sine ratios.
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If you’re using a calculator or a computer, you wanna make sure that it’s set to radians and then enter the sine inverse of 16 over 20.
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You’ll get an irrational number 0.927295 and on and on.
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Rounding this to two decimal places, to the hundredths place, we see that the digit to the right of the hundredths place is a seven; it’s a larger than five.
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So we round the hundredths place up.
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The two becomes a three and everything to the left of the hundredths place stays the same.
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Just to know, if your calculator or computer told you that the answer was 53 and 130 thousandths, you have it set to degrees.
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That is the sin inverse of 16 over 20 in degrees.
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And that’s not what we’re looking for here.
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The angle 𝜃 measured in radians is 0.93 radians.