A 175-pound force and a 230-pound force are acting on the same point in directions that differ by 42°. What is the angle that the resultant makes with

the 175-pound force?

complete the "parallelogram"

let the resultant have a magnitude of R

I see it as:
R^2 = 175^2 + 230^2 - 2(175)(230)cos138°
find R
label the angle the resultant makes with the 175 pound force be Ø

then by sine law:
sinØ/230 = sin 138°/R

find Ø

Just noticed that Steve did the same question using components

http://www.jiskha.com/display.cgi?id=1343845975

take your choice, both give 24° to the nearest degree.

To find the angle that the resultant makes with the 175-pound force, we can use the concept of vector addition. The resultant of two vectors can be found by adding them together using the parallelogram law of vector addition.

First, let's resolve both forces into their x and y components. We'll use trigonometry to do this.

The 175-pound force can be resolved as follows:
Fx1 = 175 * cos(0°)
Fy1 = 175 * sin(0°)

The 230-pound force can be resolved as follows:
Fx2 = 230 * cos(42°)
Fy2 = 230 * sin(42°)

Next, we'll add the x and y components of both forces to find the resultant components:
Rx = Fx1 + Fx2
Ry = Fy1 + Fy2

Now, we can calculate the magnitude of the resultant force:
R = sqrt(Rx^2 + Ry^2)

Finally, we can find the angle that the resultant makes with the 175-pound force using trigonometry:
θ = arctan(Ry / Rx)

By plugging in the calculated values, we can solve for θ.