# Video: Determining the Measure of an Angle Given Its Tangent Function

Find the angle 𝐴 to the nearest tenth of a degree, knowing that tan of 𝐴 = 0.86 and that 𝐴 ∈ (0°, 180°).

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### Video Transcript

Find the angle 𝐴 to the nearest tenth of a degree, knowing that tan of 𝐴 equals 0.86 and that 𝐴 falls between zero and 180 degrees.

We know that the tan of 𝐴 equals 0.86. If we’re given a tangent ratio for some angle, the tool that we use to find out what the angle would be is an inverse trigonometric function. Since we’re working with a tangent ratio, we have an inverse trigonometric function as the tan inverse, written as tangent with a superscript of negative one. You might also see this written as arctan.

We’ll take the tangent inverse of both sides of this equation. The tangent inverse of the tan of 𝐴 equals 𝐴. And we’ll find the tangent inverse of 0.86 on our calculator. We’ve been told that we want this angle in degrees. So we need to make sure that our calculator is set to calculate the tangent inverse in degrees and not in radians. When we do that, we get 𝐴 equals 40.69553 continuing. Rounding this to the nearest tenth of a degree, the digit to the right of the tenths place is a nine. And therefore, we round our angle measure up to 40.7 degrees.

If the tan of angle 𝐴 is equal to 0.86 and 𝐴 falls between zero and 180 degrees, then 𝐴 equals 40.7 degrees.