You are a surveyor. You take your first measurement facing north. You turn to the right to take your second measurement and then to right again, 4 times as far, to take your third measurement. You are now facing due west. How many degrees did you turn to take your second measurement? How many degrees should you have turned after your second measurement if you wanted to take your third measurement facing south? How many degrees must you turn to the left in order to take a fourth measurement in the opposite direction of your second measurement?

3/5

step-by-step explanation:

double number line is not a standard concept, so it must have been defined in your textbook. assume top line is numerator.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west