Question #161096

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?


1
Expert's answer
2021-02-05T04:57:18-0500

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

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

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

cosα=ESEJEJEScos \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.

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