Answer to Question #161096 in Geometry for Tatiana A.

Question

Three houses are mapped on a coordinate grid. Josh's house is located on Red Street at (- 5, - 4) . Sarah's house is located on Green Street at (). Emma's house is located on the corner of Red Street and Green Street at (4, - 3) . What is the measure of the angle (in degrees) where Red Street and the Green Street Intersect?

Answer 1

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

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

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

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

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

a = 96,34°

Solution: 96 degrees.