Please help me with math problem?

A vector A has a magnitude of 54.0 m and points in a direction 20.0° below the x axis. A second vector, B, has a magnitude of 70.0 m and points in a direction 52.0° above the x axis.


(a) Sketch the vectors A, B, and C = A + B. (Do this on paper. You do not need to turn this in,but use it as a control of your calculations.)


to find thee x and y component of vector C


as well find thee magintude and direction

Please help me with math problem?
"A" has a negative vertical (y-axis) component of:





sin(20) = -y/54


54 * sin(20) = -y


-18.46908774 = y





and a positive horizontal (x-axis) component of:





cos(20) = x/54


54 * cos(20) = x


50.74340152 = x











"B" has a positive vertical component of:





sin(52) = y/70


70 * sin(52) = y


55.16075275 = y





and a positive horizontal component of:





cos(52) = x/70


70 * cos(52) = x


43.096303 = x








Therefore, the combined vector, "C", has


components of:





x = 50.74340152 + 43.096303


x = 93.839705





y = -18.46908774 + 55.160752752


y = 36.6916650





Magnitude is the hypotenuse of the right triangle


formed by these horizontal and vertical vectors:





x^2 + y^2 = magnitude^2


(93.839705)^2 + (36.6916650)^2 = magnitude^2


8805.890196 + 1346.278281 = magnitude^2


10152.1685 = magnitude^2


100.758 = magnitude





tan(direction) = 36.6916650/93.839705


direction = atan(.391004)


direction = 21.35568 degrees