Question Video: Measuring Any Angle in a Right Triangle Using the Sine Ratio Mathematics • 11th Grade

calculate angle 𝜃, to the nearest degree.

02:02

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.