How do I find the magnitude from this data:

theta_1 = 44.9 theta_2 = 146.1
A = 4.8 cm B = 8.7 cm

of vector (A + B)

I don't know where theta 1 and theta 2 are, but have you considered drawing the figure, then using the law of sines?

theta one goes with A and theta two goes with B. I know I'm supposed to use |A+B| =sqrt[ (A+B)x^2 + (A+B)y^2 ], but I am having troubles on which numbers I have to plug in for each value.

assuming the θ values are with respect to the positive x-axis, then

A = 4.8 cos44.9 i + 4.8 sin 44.9 j = 3.40i + 3.39j
B = -7.22i + 4.85j

now just add 'em up and take ||

I keep getting the wrong answer. I got 4.42, is that wrong?

(A+B)x = -3.82

(A+B)y = 8.24

14.6 + 67.9 = 82.5
so
9.08

To find the magnitude from the given data, you can use the Pythagorean theorem. The magnitude is the length of the hypotenuse of a right triangle formed by the sides A and B.

Here are the steps to find the magnitude:

1. Square the values of A and B.
A^2 = (4.8 cm)^2 = 23.04 cm^2
B^2 = (8.7 cm)^2 = 75.69 cm^2

2. Add the squared values together.
A^2 + B^2 = 23.04 cm^2 + 75.69 cm^2 = 98.73 cm^2

3. Take the square root of the result.
magnitude = √(98.73 cm^2)
magnitude ≈ 9.94 cm

Therefore, the magnitude is approximately 9.94 cm.