SOLUTION: An Uber driver leaves home and drives 1.2km to the East to pick up a passenger. She drives 3.4km to the South and drops off the passenger. Calculate the distance (in km) and direct

Algebra ->  Trigonometry-basics -> SOLUTION: An Uber driver leaves home and drives 1.2km to the East to pick up a passenger. She drives 3.4km to the South and drops off the passenger. Calculate the distance (in km) and direct      Log On


   

Question 1157552: An Uber driver leaves home and drives 1.2km to the East to pick up a passenger. She drives 3.4km to the South and drops off the passenger. Calculate the distance (in km) and direction (as a true bearing) for the driver to return directly home.
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5420) About Me  (Show Source):
You can put this solution on YOUR website!
The home, pick-up, and drop-off points form a right triangle,
and we know the Pythagorean theorem/formula, and a little trigonometry.
The hypotenuse of that right triangle is the distance the driver has to drive to drive directly home,
and the Pythagorean theorem/formula tells us how to calculate it:
hypotenuse%5E2=%281.2km%29%5E2%2B%283.4km%29%5E2-->hypotenuse%5E2=1.44km%5E2%2B11.56km%5E2-->hypotenuse%5E2=1.3km%5E2-->hypotenuse=sqrt%281.3%29km%5E2=highlight%283.6km%29%28rounded%29
Trigonometry tells us that the ratio of length of sides opposite%2Fadjacent to an acute angle in a right triangle is the tangent of that angle.
So, tangent%28red%28alpha%29%29=1.2km%2F3.4km=6%2F17=approximately0.35294 .
Luckily, we nowadays have calculators that tell us that
if tangent%28red%28alpha%29%29=0.35294 , then red%28alpha%29=approximatelyhighlight%2819.44%5Eo%29 .
When I was is school (and college) I had to look us answers in a table of logarithms, and calculate using a slide rule.

Answer by ikleyn(53996) About Me  (Show Source):
You can put this solution on YOUR website!
.
.
I copied and pasted the solution by @KMST here.
I only fixed her typos to make the presentation error-free.


The home, pick-up, and drop-off points form a right triangle,
and we know the Pythagorean theorem/formula, and a little trigonometry.
The hypotenuse of that right triangle is the distance the driver has to drive to drive directly home,
and the Pythagorean theorem/formula tells us how to calculate it:
hypotenuse%5E2=%281.2km%29%5E2%2B%283.4km%29%5E2-->hypotenuse%5E2=1.44km%5E2%2B11.56km%5E2-->hypotenuse%5E2=13km%5E2-->hypotenuse=sqrt%2813%29 km = highlight%283.6%29 km %28rounded%29
Trigonometry tells us that the ratio of the length of the sides opposite%2Fadjacent to an acute angle in a right triangle is the tangent of that angle.
So, tangent%28red%28alpha%29%29=1.2km%2F3.4km=6%2F17=approximately0.35294 .
Luckily, we nowadays have calculators that tell us that
if tangent%28red%28alpha%29%29=0.35294, then red%28alpha%29=approximatelyhighlight%2819.44%5Eo%29.
When I was in school (and college), I had to look up answers in a table of trigonometric functions and calculate using a slide rule.