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