Question

A ship is docked at an island that is 102.5 km south and 31.4 km east of the ship’s

Answer 1

Answer:

$\theta=287^o$

Step-by-step explanation:

Position in the Plane

If we place an object in a plane and mesure its x and y coordinates, we are referencig its position according to the rectangular system. Other popular way to reference positions is in polar form or magnitude-angle form. If we have the rectangular coordinates (x,y), we can easily find the polar coordinates $(r,\theta)$ (and vice-versa). We use the formulas

$r=\sqrt{x^2+y^2}$

$\displaystyle tan\theta=\frac{y}{x}$

We have x=31.4 Km East (a positive coordinate) and y=-102.5 Km South (negative because it's pointing downwards). we need to find the angle respect to the East reference where $\theta=0^o$. Check the image below for reference.

$\displaystyle tan\theta=\frac{-102.5}{31.4}=-3.264$

$\theta=-73^o$

The angle can be also given as a positive quantity by adding 360^o

$\theta=-73^o+360^o$

$\boxed{\theta=287^o}$