Solving for Angles Using Trigonometric Ratios

8.3 Pt II - Trig Ratios/

Finding Angles

By Steve Dull

Objective

To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles.​

​We've been writing and solving equations using the trig ratios (sine, cosine, tangent) to determine missing side lengths of right triangles.

It turns out if you know the sin, cosine, or tangent ratio of an angle, you can use the inverse of the ratio (sin^-1, cos^-1, tan^-1) to find the measure of the angle.

​

In other words, if we know two sides we can determine the measures of the acute angles of the right triangle.​

You'll need to activate the "2nd" functions to do this.

Let's walk through one

​We're trying to find the value of x. (Typically the Greek letter theta Θ is used as the variable to stand for an angle measure).

​

From x the side labeled "15" is the opposite and the side labeled "24"​ is the hypotenuse.

Multiple Choice

Which trig ratio is made up of the opposite and hypotenuse?

• sine

• cosine

• street sign

• exit sign

​Back in the day we'd do 15 /24, get 0.625, then try to find that on a trig table.

​

(Somewhere between 38°​ and 39°, right?

Modern-day equivalent:

Use the inverse sine function

Your turn

Open Ended

Determine the value of x. Type your answer and upload a snap of your work.

One more

Multiple Choice

• $$71.3$$  

• $$18.7$$  

• $$17.8$$  

• $$72.2$$  

Independent practice

​Complete #11-14 and #18 on your notes page