# Question Video: Finding the Measure of the Angle between Two Straight Lines given Their Slopes Mathematics

Determine to the nearest second, the measure of the angle between two straight lines having slopes of 5 and 1/4.

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### Video Transcript

Determine to the nearest second the measure of the angle between two straight lines having slopes of five and one-quarter.

Knowing the slopes of our two lines, that’s 𝑚 one is equal to five and 𝑚 two is one-quarter, we can find the acute angle 𝛼 between the lines using the formula tan 𝛼 or the tangent of 𝛼 is the absolute value of 𝑚 one minus 𝑚 two over one plus 𝑚 one multiplied by 𝑚 two. In our case, this gives us the tan of 𝛼 is the absolute value of five minus one over four all divided by one plus five times one over four. The right-hand side evaluates to 19 divided by nine. So this is the tan of our angle 𝛼. And now taking the inverse tangent on both sides, we have 𝛼 is equal to the inverse tan of 19 over nine. And from our calculators, we find to four decimal places that 𝛼 is 64.6538 degrees.

We’re asked to find the angle to the nearest second. And to do this, we recall that there are 60 minutes in one degree and 60 seconds in one minute. We begin therefore by multiplying the decimal part of our degrees by 60, and this gives us to four decimal places 39.2294 minutes. Now, multiplying the decimal part of our minutes by 60 to four decimal places, this gives us 13.7666 seconds, which is approximately 14 seconds. To the nearest second then, the angle between our two straight lines is 64 degrees, 39 minutes, and 14 seconds.