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Chapter 5: Problem 44

What is the angle between the positive horizontal axis and the line containing the points (2,5) and (6,2)\(?\)

Short Answer

Expert verified
The angle \(\theta\) between the positive horizontal axis and the line containing the points (2, 5) and (6, 2) is \(\arctan\left(\dfrac{-3}{4}\right) \times \dfrac{180^\circ}{\pi\ \mathrm{radians}}\). Use a calculator to find the arctan value and then multiply it by the conversion factor to obtain the angle in degrees.

Step by step solution

01

Find the slope of the line containing the two points

To find the slope of the line containing the points (2, 5) and (6, 2), we can apply the formula \(m = (y2 - y1)/(x2 - x1)\), where \((x1, y1) = (2, 5)\) and \((x2, y2) = (6, 2)\). \(m = \dfrac{(2-5)}{(6-2)} = \dfrac{-3}{4}\)
02

Find the angle using arctan

Now, we can use the inverse tangent function to find the angle. Let the angle be \(\theta\). \(\theta = \arctan(m) = \arctan\left(\dfrac{-3}{4}\right)\)
03

Convert the angle to degrees

The arctan function typically returns a value in radians. To find the angle in degrees, we can use the conversion factor \(180^\circ/\pi\ \mathrm{radians}\). \(\theta = \arctan\left(\dfrac{-3}{4}\right) \times \dfrac{180^\circ}{\pi\ \mathrm{radians}}\) Now, you can use a calculator to find the arctan value and then multiply it by the conversion factor to obtain the angle between the positive horizontal axis and the line containing the points (2, 5) and (6, 2) in degrees.

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