A Formula for Tangents

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A formula with tangents will require you to pay close attention to the value of X. Find out about a formula for tangents with help from an experienced math professional in this free video clip.

Part of the Video Series: Math Skills
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Video Transcript

Hi, I'm Drew Moyer and this is a formula for tangents. Suppose I'm given this diagram, and I'm told to find the link of the tangent line, or X. The first thing I wanna do is connect this radius, all the way up to the point of tangency. And, because of the theorem, I know that the radius must be perpendicular to the tangent line at the point of tangency. So, this is a right angle, and, since I'm given that this radius is 10, all radii are congruent, which means this radius is also 10. And, from there, you can see that I have a right triangle set up, and all I have to do is use it in Pythagorean theorem to solve for X. So, I'm gonna take the shortest side, 10 squared plus X squared, my other leg, is equal to the hypotenuse square, which 10 plus 16 is 26, squared. So, to simplify after that, and I have a hundred, plus X squared is equal to 676. Subtract a hundred from both sides, X squared is equal to 576, and then, I wanna take the square root of both sides, and I'm left with X equals 24. So, now I know the length of this tangent line is 24. I'm Drew Moyer, and this is a formula for tangents.


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