Question

1. a line goes through the points (0, 0) and (x, 12). if the slope angle of the line is 42°, what is the x - coordinate of the point?

Explanation:

Step1: Recall the slope formula

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(x,12)\), so \(m = \frac{12-0}{x - 0}=\frac{12}{x}\).

Step2: Recall the relationship between slope and slope - angle

The slope \(m\) of a line with slope - angle \(\theta\) is \(m=\tan\theta\). Given \(\theta = 42^{\circ}\), so \(m=\tan(42^{\circ})\approx0.9004\).

Step3: Equate the two expressions for slope

Since \(\frac{12}{x}=\tan(42^{\circ})\), we can solve for \(x\). Cross - multiply to get \(x=\frac{12}{\tan(42^{\circ})}\).

Step4: Calculate the value of \(x\)

Substitute \(\tan(42^{\circ})\approx0.9004\) into the equation \(x=\frac{12}{0.9004}\approx13.33\).

Answer:

\(x\approx13.33\)