Question Video: Using Inverse Trigonometric Functions to Solve a Trigonometric Equation Mathematics

Given that 𝐴 is an acute angle and sin 𝐴 = 0.8193, determine 𝑚∠𝐴 to the nearest tenth of a degree.

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Video Transcript

Given that 𝐴 is an acute angle and sin 𝐴 is equal to 0.8193, determine the measure of angle 𝐴 to the nearest tenth of a degree.

We know that sin of some unknown angle 𝐴 is equal to 0.8193. If we think about this trig function, the 𝜃-value is an angle measure, and it’s equal to some ratio of side lengths. If we know the ratio of side lengths and we want to know the angle measure, we need a function that can undo the sine function, and that would be the sin inverse of the sin 𝜃. We’ll need to take the inverse sin of sin 𝐴. So, we’ll do that to both sides of our equation. The sin inverse of sin 𝐴 is just equal to 𝐴, and the sin inverse of 0.8193 can be found with a calculator. Make sure that your calculator is set to degrees, since we’re interested in this angle measure in degrees.

When we do that, we get 55.0147 continuing degrees. We’ll round this to the nearest tenth, and we’ll see that the measure of angle 𝐴 is 55.0 degrees. We’ve been given that 𝐴 is an acute angle, and so we’re only interested in the smallest value that 𝐴 can be, which here is 55 degrees.

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