Asked by Hanky

A car travels 59.5 miles at 53.0° S of W. The car then makes a 90.0° turn to the left and travels an additional 90.3 miles. What is the car's final displacement?

I have set up the diagram, and I believe I am supposed to use the pythagorean theorem.

Well let me reverse that, I can use the pythagorean theorem because 59.5 m and 93.0 m was given to me, but I was also given an angle 53°. Honestly I'm not exactly sure how to approach this question. BUT I do believe I made my diagram correctly which I put on pasteboard( nevermind I am not allowed to post links )
Answered by Hanky
well, this was what I decided to go with.

since it has designated that he made a 90° turn; We can indicate that it is a right triangle. So, I performed this:

√( (59.5)^2 + (93.0)^2 )
Answered by Hanky
Whoops sorry forgot to give my value after doing the calculation. My answer is: 110.4 miles, the miles squared gets square rooted so then it becomes just miles, right?
Answered by Damon
Remember it did not just ask for distance (scalar) but also direction (vector).
Answered by Damon
But good job so far Hanky.
Answered by Hanky
Ok, so I am guessing I need to use the angle given to me. Now I have to find the hypotenuse length and angle? I think?
Answered by Damon
the angle counterclockwise from west is 53 + tan^-1(90.3/59.5)

that will end up in quadrant 4, east of south
Answered by Damon
53 + 56.6 counterclockwise from west
or 109.6
which is 109.6 - 90 = 19.6 degrees east of South
Answered by Hanky
if I did it my way, would I be taking steps to solve the problem?
Answered by Hanky
or actually that is what you said, sorry.
Answered by Damon
I thought I did it your way :)
All I did was get the angle, you got the distance (hypotenuse)
Answered by Hanky
Ok thank you!

I accidentally miscalculated my hypotenuse... so now my final answer is:
108.14 miles 56.6°East of South, because it passes the third quadrant by 19.6° which is why you subtracted 90°
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