Video: Using Inverse Trigonometric Functions to Solve Trigonometric Equations

If 𝐸 is an acute angle, find the value of 𝑚∠𝐸 given sin 𝐸 = 0.791. Give your answer to the nearest second.

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Video Transcript

If 𝐸 is an acute angle, find the value of the measure of angle 𝐸, given the sin of 𝐸 is equal 0.791. Give your answer to the nearest second.

So in order to find the measure of angle 𝐸, we need to use the inverse of sine. And now we plug in 0.791, and that’s approximately 52.27906148 degrees. However, it says give the answer to the nearest second. Now this is not a decimal place. This is something different. There are 60 minutes in each degree and 60 seconds in each minute. The angles listed in degrees can be expressed in degrees, minutes and seconds by multiplying the fractional portion of the degrees by 60 to get the number of minutes. If there’s a fractional minute, multiply that by 60 to get the number of seconds.

So we need to take our fractional portion, and we need to multiply that by 60. And we get 16.743688. So 16 would be the number of minutes. Now again, there is a fractional portion, so we need to take that and also multiply by 60 to get the number of seconds. And when multiplying by 60, we get 44.62138. Now since we are rounding to the nearest second, we need to round this number. So 44.6, the six will round the four up to a five, so we have 45 seconds.

Therefore, the measure of angle 𝐸 would be 52 degrees, 16 minutes, 45 seconds.

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