Question

Three houses are mapped on a coordinate grid.

Josh's house is located on Red Street at (-10,-5).

Sarah's house is located on Green Street at (-5,-6).

Emma's house is located on the corner of Red Street and Green Street at (0,4).

What is the measure of the angle in degrees) where Red Street and the Green Street intersect?

Answer 1

Explanation:

Let us consider the task to find the angle between vectors ES and EJ (the first letters are taken to name the vectors).

\overrightarrow{ES} = (4;4) - (4; -3) = \overrightarrow{(0; 7)}

ES

=(4;4)−(4;−3)=

(0;7)

​

\overrightarrow{EJ} = (-5; -4) - (4; -3) = \overrightarrow{(-9; -1)}

EJ

=(−5;−4)−(4;−3)=

(−9;−1)

​

cos \alpha=\frac{\overrightarrow{ES}*\overrightarrow{EJ}}{|\overrightarrow{EJ}|*|\overrightarrow{ES}|}cosα=

∣

EJ

∣∗∣

ES

∣

ES

∗

EJ

​

cos(a) = (0*(-9)+7*(-1)) / (7*9.055) = -0.11043;

a = 96,34°

Solution: 96 degrees.