Video Transcript
Find the length of the line segment
๐ด๐ถ, given that ๐ด๐ต๐ถ is a right triangle at ๐ต, where sin of ๐ถ equals nine over
16 and ๐ด๐ต equals 18 centimeters.
In this case, the first step should
be to sketch a right triangle that meets these conditions. We have a right triangle. The right angle is at ๐ต, so we
label the right angle ๐ต. And then we add on ๐ด and ๐ถ. Weโre told that ๐ด๐ต measures 18
centimeters. And then we have this other piece
of information that sin of ๐ถ equals nine over 16. This tells us that the angle weโre
working with is angle ๐ถ. And if we think of our acronym SOH
CAH TOA, we know that the sine of an angle is equal to the opposite over the
hypotenuse.
If the angle weโre considering is
๐ถ, the opposite will be the side ๐ด๐ต, and the hypotenuse is always the side
opposite the right angle. Itโs the side ๐ด๐ถ. And so that ratio is nine over
16. The key thing to remember here is
that these relationships are ratios. And so sin of angle ๐ถ tells us
that for every nine units on the opposite side length, there will be 16 units on the
hypotenuse side length.
So we can say that if there are 18
centimeters on the opposite side, we know that nine times two equals 18. And when dealing with ratios or
fractions, if we multiply by two in the numerator, we need to multiply by two in the
denominator. 16 times two is 32. And so we can say that if the
opposite is 18, the hypotenuse must be 32. Line segment ๐ด๐ถ is the
hypotenuse, and it measures 32 centimeters.
