# Math Help - Trigonometric Word Problems involving Vectors, Magnitude, and Direction!

1. ## Trigonometric Word Problems involving Vectors, Magnitude, and Direction!

Hi all, I have recently asked about a couple problems involving law of sines/cosines and I understand those now thanks to the help I've received here! Now I've run into a word problem involving magnitude and direction. I'm a bit confused on this topic, so if anyone would like to help me work a couple problems I would really appreciate it!

(1.) Two forces F1 of magnitude 35 newtons (N) and F2 of magnitude 55 newtons, act on an object at angles of 45 degrees and -60 degrees (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is, find F1+F2. Round the direction and magnitude to two decimal places.

When I asked my professor about these problems he told me "I'll have to get back to you on that, just read the book until you get it"

(2.) Two forces of magnitude 25 pounds and 40 pounds act on an object. The force of 40 lb acts along the positive x-axis, and the force of 25 lb acts at an angle of 80 degrees with the positive x-axis. Find the direction and magnitude of the resultant force. Round the direction and magnitude to the nearest whole number.

2. Originally Posted by mdebourg
Hi all, I have recently asked about a couple problems involving law of sines/cosines and I understand those now thanks to the help I've received here! Now I've run into a word problem involving magnitude and direction. I'm a bit confused on this topic, so if anyone would like to help me work a couple problems I would really appreciate it!

(1.) Two forces F1 of magnitude 35 newtons (N) and F2 of magnitude 55 newtons, act on an object at angles of 45 degrees and -60 degrees (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is, find F1+F2. Round the direction and magnitude to two decimal places.

When I asked my professor about these problems he told me "I'll have to get back to you on that, just read the book until you get it"

(2.) Two forces of magnitude 25 pounds and 40 pounds act on an object. The force of 40 lb acts along the positive x-axis, and the force of 25 lb acts at an angle of 80 degrees with the positive x-axis. Find the direction and magnitude of the resultant force. Round the direction and magnitude to the nearest whole number.

use components to add the vectors ...

(1) $R_x = 35\cos(45) + 55\cos(-60)$

$R_y = 35\sin(45) + 55\sin(-60)$

$|R| = \sqrt{(R_x)^2 + (R_y)^2}$

$\theta = \arctan\left(\frac{R_y}{R_x}\right)$

same procedure for #2