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Chapter 6: Problem 31

Find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. $$(-2,20),(10,0)$$

Short Answer

Expert verified
The inclination of the line passing through the points (-2,20) and (10,0) is \(-arctan(\frac{5}{3})\) radians or \(-arctan(\frac{5}{3}) * \frac{180}{\pi}\) degrees.

Step by step solution

01

Find the Slope

The slope (m) of a line passing through points \(A(x_1, y_1)\) and \(B(x_2, y_2)\) is given by \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Given points A(-2,20) and B(10,0), apply the formula to find the slope. So, \(m = \frac{0 - 20}{10 - (-2)} = -\frac{20}{12} = -\frac{5}{3}\).
02

Calculate Angle of Inclination in Radians

The inclination of this line \(\Theta\) is calculated by taking the tangent inverse of the slope, also known as arctan or tan^-1. So, \(\Theta = arctan(m)\). Apply the slope calculated in the first step: \(\Theta = arctan(-\frac{5}{3})\). Therefore, \(\Theta = -arctan(\frac{5}{3})\).
03

Convert from Radians to Degrees

To convert from radians to degrees, use the formula: degrees = radians * \(\frac{180}{\pi}\). Therefore, \(\Theta = -arctan(\frac{5}{3}) * \frac{180}{\pi}\).

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