Chapter 4, Problem 19RP

To determine

To calculate: To find measure of largest angle .

Answer to Problem 19RP

${90}^{\circ }$

Explanation of Solution

Given information: P (3, 6), Q (4, 1), R (14, 3).

Formula used : Angle sum property of triangle ; if two lines are perpendicular then product of their slops is -1, Slope of the line joining (x₁,y₁) and (x₂,y₂) is $\frac{y_2-y_1}{x_2-x_1}.$

Calculation:

Slope of $PQ=\frac{1-6}{4-3}=-5$

And Slope of $QR=\frac{3-1}{14-4}=\frac{1}{5}$

Hence $QR\perp PQ.$

I.e. Measure of $\angle Q$ is ${90}^{\circ }$ which is the largest angle of right angle is largest in a right triangle .