TRIGONOMETRY: How to find distance and direction?

Question

A hawk takes flight from a mountain peak and flies 800 meters west. Then it takes a turn and flies 200 meters south. What is the distance and direction of the hawk from the mountain peak?

Answer 1

In order to find the distance we need to use the Pythagoras theorem

 

d^2 = 800^2 + 200^2

 

d= 824.6 m

 

 

we can find the direction by using the eq for a tangent

 

he opposite side is 200 m and the adjacent side is 800m 

 

tan theta = opposite / adjacent

 

theta = arc tan (800/200)

 

 

The hawk is at a distance of 824.6m flying at an angle 76 degrees NE of the mountain peak.

Answer 2

The final location will be southwest of the mountain peek.

 

The distance from the peak is the length of the hypotenuse below:

 

 

*

| \

|  \     

|   \    

|a  \  c 

|     \  

|      \ 

|____\

    b

 

a²+b²=c²

a = 200

b=  800

c = √(200²+800²⁾ =  824.62 

 

So the hawk has flow 824.62 meters southwest of the mountain peak.