Answer:
(a) θ = 33.86°
(b) Ay = 49.92 N
Explanation:
You have that the magnitude of a vector is A = 89.6 N
The x component of such a vector is Ax = 74.4 N
(a) To find the angle between the vector and the x axis you use the following formula for the calculation of the x component of a vector:
(1)
Ax: x component of vector A
A: magnitude of vector A
θ: angle between vector A and the x axis
You solve the equation (1) for θ, by using the inverse of cosine function:

the angle between the A vector and the x axis is 33.86°
(b) The y component of the vector is given by:

the y comonent of the vecor is Ay = 49.92 N
The given mass is 0.025563 g.
Examine the given choices.
a. 0.026 g
This uses 2 significant digits, with rounding to the 3rd decimal place.
b. 2.5 x 10² g = 250 g.
It is incorrect.
c. 0.025 g.
This uses 2 significant digits. It is inaccurate because it does not use rounding to the 3rd decimal place.
d. 0.02 g
This uses one significant digit. It is incorrect for representing the given data.
Answer: a. 0.026 g