### Video Transcript

Find the length of line segment
π΄πΆ given π΄π΅πΆ is a right-angled triangle at π΅, where sin of πΆ equals nine over
16 and π΄π΅ equals 18 centimeters.

In this case, the first step should
be to sketch a right triangle that meets these conditions. First, we have a right
triangle. The right angle is at π΅. So we label our right angle π΅. And then we add π΄ and πΆ. Weβre told that π΄π΅ measures 18
centimeters. And then we have this other piece
of information that sin of πΆ equals nine over 16. This tells us that the angle weβre
talking about is angle πΆ. And if we think of our trig ratio
acronym SOHCAHTOA, we know that the sin of an angle is equal to the opposite over
the hypotenuse. And so if the angle weβre
considering is πΆ, the opposite side length will be the side π΄π΅. And the hypotenuse is always the
side opposite the right angle. And so that relationship is 9 to
16.

The key thing to remember here is
that these relationships are ratios. And so sin of angle πΆ 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 as 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 could say that the
hypotenuse must measure 32 centimeters. Line segment π΄πΆ is the
hypotenuse. And that measures 32
centimeters.