Find the magnitude of the sum
of these two vectors: :
14m
30.0°
60.00
magnitude (m)

Explanation:

Sum of Vectors in the Plane

Given two vectors

They can be expressed in their rectangular components as

The sum of both vectors can be done by adding individually its components

If the vectors are given as a magnitude and an angle , each component can be found as

The first vector has a magnitude of 3.14 m and an angle of 30°, so

The second vector has a magnitude of 2.71 m and an angle of -60°, so

The sum of the vectors is

Finally, we compute the magnitude of the sum

most voltage drop calculators want the distance between the source and destination. then internally, they double it so both the source and return wires are calculated. but you need to know which distance the calculator uses so you're not half of what you should be or double what you should be.

most circuit breakers will not take a #6 directly, so the electrician will have to splice on a smaller pigtail. you also have to upsize the grounding wire when you upsized the ungrounded (hot) wire (see note in 250.122). this will preclude using most cable assemblies, as a cable with #6 copper will most likely only have a #10 grounding conductor. you need a #6 grounding conductor if the circuit is 20a. a #8 cable is no better, as it will have a #10 grounding conductor too. but most 20a breakers will take a #8 directly.

in your related post, you didn't say what type of load this is. if it is a light or heater, voltage drop won't be a big issue. if this is a motor, the current needs are huge at startup and the voltage drop can pose a problem. if this is a motor, knowing if the motor is under much load during startup will answer the voltage drop effect (a saw is easier to start than a compressor).