How to Solve a Tangent Ratio

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Solving a tangent ratio involves dealing with a right triangle. Learn how to solve a tangent ratio with help from an experienced educator in this free video clip.

Part of the Video Series: Lessons in Math
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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to tell you how to solve a tangent ratio. So if we're dealing with tangent of course we're going to be dealing with a right triangle. So we're going to start by drawing a right triangle and we'll draw our theta and let's leave our right triangle 3, 4, 5. So if I wanted to know the tangent of theta I'm going to remember that the ratio for tangent is going to be my opposite side over my adjacent side, right? Sohcahtoa, that's the last part of it. So I look at my theta and I'm looking for the opposite side and the easiest way to find the opposite side is go to your angle and just draw a line straight across and 4 is my opposite side. So 4 is going to be in my numerator. My adjacent side is going to be 3 because remember even though 5 is also adjacent to theta, 5 is the hypotenuse so we don't consider that the adjacent side. So 3 is my adjacent side. So that means that the tangent of theta is 4/3. Now if I wanted to go on and find out what theta is, then what you're going to do in your calculator is you're going to do the inverse function of tangent so you're going to hit shift tangent so that you get tangent with a negative 1 as the exponent, put in 4/3 and you'll find out what the measure of the angle is that has 4/3 as a tangent. My name is Marija and I just showed you how to do the tangent ratio.

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