An airplane flies 200 km due west from city a to city b and then 275 km in the direction of 26.0° north of west from city b to city c. (a) in straight-line distance, how far is city c from city a?
relative to city a, in what direction is city c?
(c) why is the answer only approximately correct?

(a) 463.13 km, approximately

(b) 15.09° north of west, approximately

(c) Is only approximately correct because its calculation involves trigonometric functions and square roots that, in this case, cannot been simplified, but rounded.

Explanation:

By depicting a triangle ABC,

(a) the length AC is given by

(b)

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =