Let a be the vector of length 125 that when drawn in standard position makes a 144° angle with the positive x-axis. let b be the vector of length 39 that when drawn in standard position makes a 302° angle with the positive x-axis. find the length of v = a + b and the angle θ that v makes with the positive x-axis when drawn in standard position. round your approximations to three decimal places.

The length is 90.033 and the angle that v makes with the positive x-axis is 153.339°

Step-by-step explanation:

Firstly we will have to convert our given vectors to their rectangular Cartesian vector form as follow,

Now that we have these, we can add them to obtain v as follows,

Now that we have the Cartesian vector form we can calculate its length and its direction with respect to the positive x-axis as follows(In fact we usually refer the angles from the positive x-axis),

So the length of the vector is 90.033 and the angle it makes with the positive x-axis is 153.339°.

step-by-step :