Answer:[tex]22.62^{\circ},1.2\ \text{miles}[/tex]
Step-by-step explanation:
Given
Jeremy takes road and ride 3.6 miles to the east and then 1.5 miles to the north
If there is a path that goes through the woods directly from Jeremy's house to Khaleel's house with length x(say)
From the figure, we can write the angle between road and the path
[tex]\Rightarrow \tan \theta=\dfrac{1.5}{3.6}\\\\\Rightarrow \tan \theta=0.4167\\\Rightarrow \theta=22.62^{\circ}[/tex]
(b)Length of the path is
[tex]\Rightarrow x=\sqrt{3.6^2+1.5^2}\\\Rightarrow x=\sqrt{15.21}\\\Rightarrow x=3.9\ miles[/tex]
Distance covered by the road is [tex]3.6+1.5=5.1\ miles[/tex]
Difference between the two lengths is
[tex]\Rightarrow 5.1-3.9=1.2\ \text{miles}[/tex]
