What is the direction and magnitude of the net force acting on the hot air balloon? It has an arrow up with 6300, an arrow down with 3200, an arrow to the right of 1350 and an arrow left with 745.

Question

Is this how to do it and if so, how do I convert the sin of theta into degrees.

6300-3200=3100 up
1350-605=745 right
31002+7452=x2
approximately 3188.26
745/3188.26=.234

Answer 1

Yeah, you have the right process.

After you calculate the net force in x and y directions, construct a right triangle by drawing your vectors head-to-tail.

|------
| /
| /
| /
| /
theta

The hypotenuse has a length of ~3188 by Pythagorean theorem.

To calculate the angle, we use trig.
tan(theta) = opposite / adjacent
theta = arctan(745 / 3100) = 13.5 deg

So your final answer is 3188N @ 13.5 degrees [East of North].

Answer 2

thank you

Answer 3

X = 1350-745 = 605 N.
Y = 6300-3200 = 3100 N.

Fn = Sqrt(X^2+Y^2) = Sqrt(605^2+3100^2) = 3158.5 N.

Tan A = Y/X = 3100/605 = 5.12397.
A = 79o N. of E. = Direction.