Question

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)?

Answer 1

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

Answer 2

150²+170²-2*150*170cos(139.17)° ?

Answer 3

@campbell_st

Answer 4

@freckles

Answer 5

@Nnesha @jdoe0001

Answer 6

actually, as @cambell_st is correct
the angle shown there, is just a portion of the 90 degrees

and you can use the law of cosines to find the missing side, or distance to the airport

Answer 7

150²+170²-2*150*170cos(139.17)°

would this be the right way to input the values?

Answer 8

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

Answer 9

would the answer be 226 miles?

Answer 10

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

Answer 11

hmmm nope, is a bit more

Answer 12

okay, ill recalculate

Answer 13

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

Answer 14

https://www.google.com/search?client=opera&q=sqrt(150%5E2%2B170%5E2-2*150*170*cos(139.17+degrees))&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest&gws_rd=ssl

Answer 15

i got a negative when i did cos(139.17)

Answer 16

so it would be 300 miles?