Video: Using Right-Angled Triangle Trigonometry to Solve Word Problems with Diagrams

The height of a ski slope is 16 metres and the length is 20 metres. Find the measure of ∠𝜃 giving the answer to two decimal places.

03:30

Video Transcript

The height of a ski slope is 16 metres and the length is 20 metres. Find the measure of angle 𝜃 giving the answer to two decimal places.

Our question here is actually pretty straightforward. The only thing is we need some information outside of the information that was given in our question. We’ll need to use a trig function. Sine function would be the opposite side length over the hypotenuse, the cosine function would be using the adjacent side length over the hypotenuse, and our tangent function would be using the opposite side length over the adjacent side length. Which function fits best here?

Our starting point is this angle. It’s the angle we’re looking for. And 16 metres is the side length that’s opposite the angle we’re given and the 20 metres side is the hypotenuse. We know that it’s the hypotenuse because it’s the side length that’s across from the right angle. We have an angle, we have the opposite side length, and we know the hypotenuse. So which trig function should we use? We should use our sine function. We have all the information to use the sine function.

Now, let’s plug in the information that we know. Since sine of 𝜃 is the opposite over the hypotenuse, we add 16 metres as the numerator and 20 metres as the hypotenuse. But now, we’re at a little bit of a dead end. How do we go from this ratio to an angle measure? We need another function. We need the inverse sine.

The sine inverse takes the ratio of the opposite side length over the hypotenuse and gives us an angle measure. Using the sine inverse would look like this: sine to the negative one of 16 over 20 equals 𝜃 — equals our angle measure. If I plug that into the calculator sine inverse of 16 over 20, I get 53.130102 continuing.

Our question is asking us to give the angle measure accurate to two decimal places. We noticed that our third decimal place is a zero. So the 13 hundredths would stay the same. The three would stay the same. Our angle measure is 53 and 13 hundredths. But we don’t wanna forget that we’re talking about degrees. So it’s 53 and 13 hundredths degrees.

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