Video Transcript
We have a right-angled triangle
in which we’re given the lengths of two sides. And we’re asked to calculate
angle 𝜃 to the nearest degree.
So, as with any problem for
trigonometry, my first step is to label all three sides of the triangle in
relation to this angle 𝜃. So, we have the opposite, the
adjacent, and the hypotenuse. Now, looking at this triangle,
I can see that it’s the sine ratio that I need because I’ve been given the
lengths of the opposite and the hypotenuse. So, that is O and H, which is
the SOH part of SOHCAHTOA. Now, in this video, they’re all
going to be involving sine because that’s specifically what the video is
about. But in general, if you didn’t
know which of the ratios to use, that’s how you would work it out, by
determining which pair of sides is involved in the ratio.
So, I recall the definition of
sine, which is that sin of the angle 𝜃 is equal to the opposite divided by the
hypotenuse. And now, I’m gonna write down
this ratio for this particular triangle. So, I have that sin of 𝜃,
which is unknown, is equal to nine over 16. So, I know the value of the
ratio. And I want to work backwards in
order to find the angle that this ratio belongs to. So, this is why I’m going to
use that inverse sine function that we talked about.
And this tells me that this
angle 𝜃 is equal to the inverse sin of nine over 16. So, I need to use my calculator
to evaluate this. And remember, you may need to
use shift in order to get to that sine inverse button. But that will depend on your
calculator. And when I type this in, I will
get a value of 34.22886 for 𝜃. Now, I’m asked for 𝜃 to the
nearest degree. So, I need to round my
answer. And doing so then, tells me
that 𝜃 is equal to 34 degrees.
So, for this question then, we
identified that it was the sine ratio we needed because we had the opposite and
the hypotenuse. We wrote down the ratio for
this question. And then, we used the inverse
sine function in order to calculate this missing angle 𝜃.
