Answer:
35°
64.267 ft
78.455 ft
Step-by-step explanation:
The given situation can be modeled as a right triangle (see attached).
The interior angles of a triangle sum to 180°
⇒ angle at Jamie's position = 180° - 90° - 55° = 35°
To find the other measures (distances), we can use trig ratios.
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse
To find the distance from Rachael to Jamie:
[tex]\implies \sf \tan(55^{\circ})=\dfrac{x}{45}[/tex]
[tex]\implies \sf x=45\tan(55^{\circ})[/tex]
[tex]\implies \sf x=64.267\:ft\:(nearest\:thousandth)[/tex]
To find the distance from Lance to Jamie:
[tex]\sf \implies \cos(55^{\circ})=\dfrac{45}{y}[/tex]
[tex]\sf \implies y=\dfrac{45}{\cos(55^{\circ})}[/tex]
[tex]\sf \implies y=78.455\:ft\:(nearest\:thousandth)[/tex]
