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%Start Excel TAN Function: How to Find the Tangent Angle GA
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lifewire's editorial guidelines Updated on January 21, 2021 Tweet Share Email Tweet Share Email
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Expand Jump to a Section What's the Tangent Angle? Finding the Tangent Angle Using ASIN and ACOS Why Use ATAN ACOS or ASIN If you're working with any triangle with a right angle in it somewhere, it's simple to find the tangent angle, so long as you know the length of two sides of the triangle. Doing so is even easier in Microsoft Excel because there are built-in functions you can use.
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Information in this article applies to Excel for Microsoft 365, Excel 2019, 2016, 2013, 2010, and Excel for Mac.
What Is the Tangent Angle
A tangent angle is an angle in the triangle where you know the length of the side opposite the angle and the side adjacent to it.
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Imagine, for example, that your boss tells you to adjust a ladder at precisely 70 degrees from the ground. Unless you have some special tools, it would be complicated to measure whether the angle between the ladder and the ground is exactly 70 degrees.
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Bernard Van Berg / Getty Images However, if you have a measuring tape, you could measure the distance from the bottom of the ladder to the wall. Since the ladder against the wall forms a triangle, this would be the side that's adjacent to the tangent angle you're trying to calculate.
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Next, you'd measure the distance from the bottom of the wall to where the top of the ladder touches it. This is the distance of the side that's opposite from the tangent angle. With the measurement of the opposite and adjacent sides, you can calculate the angle at the ladder base using the arctangent function.
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If the wall (opposite) side is 10 feet, and the ground (adjacent) side is 5 feet, the formula for the tangent angle is the opposite side divided by the adjacent side. This is 10 divided by 5, or 0.5. To find the value for the angle, you need to take the arctangent of 0.5.
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Find the Tangent Angle With Excel
You could find a calculator that calculates the arctangent of a value, but Excel has a built-in function called ATAN that you can use. The formula returns the angle in radians, which your boss probably won't understand.
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You'll want to convert radians to degrees by multiplying it by 180/pi. Excel also has a PI function you can use for this purpose. The answer, in this case, is 63.43 degrees.
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This means you'll need to adjust one of the lengths until the angle is precisely 70 degrees. Doing this is easy in Excel because you can change the opposite side's value until the arctangent result is 70.
Using ASIN and ACOS in Excel
In this same scenario, let's say you don't have a tape measure long enough to measure the wall.
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You only know that the ladder is 15 feet and that it's placed five feet from the wall. Excel has two other functions that you can use to calculate the angle. The ladder's length is the hypotenuse of the triangle, and the ground distance is the adjacent side to the angle.
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So long as the triangle has one right (90 degree) angle, the information you have determines the formula you need to use. Cosine: Calculate the cosine angle if you know the length of the hypotenuse and the adjacent side.Sine: Calculate the sine angle if you know the length of the hypotenuse and the opposite side.
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In this case, the angle is the arccosine of the adjacent side divided by the hypotenuse. Since you know the adjacent side (the ground distance) is 5 feet, and the ladder length (hypotenuse) is 15 feet, the cosine of the angle is 5 divided by 15, or 0.333.
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To calculate the angle, use the arccosine formula in Excel. The result of the arccosine function is Excel is in radians, so you need to multiply it by 180/PI to convert it to degrees.
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For a 15 foot ladder with its base 5 feet from the wall, the angle is 70.53 degrees. If you knew that the height of the wall (the opposite side) is 10 feet, instead of the ground distance from the wall (the adjacent side), you'd use the arcsine formula in Excel. In this case, the sine of the angle is the opposite side divided by the hypotenuse.
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After converting to degrees, the angle, in this case, would be 48.12 degrees.
Why Use ATAN ACOS or ASIN
Here are a few examples of situations where you may need to use one of these functions in Excel: In carpentry and construction, angles and lengths are used in all aspects of building houses and buildings.
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Photographers use angles to align lighting and their creative shots carefully. In sports, understanding angles can enhance skills and improve strategy. Ships and airplanes are located on radar using angles and distances.
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If you want to be sure furniture will fit right in your room, you'll need to know how to calculate lengths and angles. You may be able to accomplish these calculations on a scientific calculator. But if you don't have one handy, Excel can help you make those calculations.
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