## anonymous one year ago An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)?

1. anonymous

2. campbell_st

the angle that includes the angle is 90 + 49.17 = 139.17 so then you can use the law of cosines to find the distance Plane to Airport

3. anonymous

150²+170²-2*150*170cos(139.17)° ?

4. anonymous

@campbell_st

5. anonymous

@freckles

6. anonymous

@Nnesha @jdoe0001

7. anonymous

actually, as @cambell_st is correct the angle shown there, is just a portion of the 90 degrees|dw:1441064992008:dw| and you can use the law of cosines to find the missing side, or distance to the airport

8. anonymous

150²+170²-2*150*170cos(139.17)° would this be the right way to input the values?

9. anonymous

yes just don't forget, you need to take the square root of that that is $$\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {\color{blue}{ a}}^2+{\color{red}{ b}}^2-(2{\color{blue}{ a}}{\color{red}{ b}})cos(C)\\ \quad \\ c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2{\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}$$

10. anonymous

would the answer be 226 miles?

11. anonymous

well $$\bf c = \sqrt{{\color{blue}{ 150}}^2+{\color{red}{ 170}}^2-(2\cdot {\color{blue}{ 150}}\cdot {\color{red}{ 170}})cos(139.17^o)}$$

12. anonymous

hmmm nope, is a bit more

13. anonymous

okay, ill recalculate

14. anonymous

well.. notice, the angle is in Degrees, thus, make sure when getting the cosine, your calculator is in Degree mode, as opposed to Radian

15. anonymous
16. anonymous

i got a negative when i did cos(139.17)

17. anonymous

so it would be 300 miles?