Question

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

Answer 1

Answer:

“Even the worst days have an ending, and the best days have a beginning.” ...

Answer 2

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.