Two forces

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Result

α =  60.19 °
m =  19.41

Solution:

$F= F_1 + F_2 \ \\ x = F_{x1} + F_{x2} \ \\ y = F_{y1} + F_{y2} \ \\ \ \\ x = 25 \sin(10^\circ )+30\sin(100^\circ ) = 19.41 \ \\ y = 25\cos(10^\circ )+30\cos(100^\circ ) = 33.89 \ \\ \alpha = \arctan \dfrac{y}{x} = 60.19 ^\circ \ \\$
$r = \sqrt{x^2 + y^2 } = 19.41$

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Following knowledge from mathematics are needed to solve this word math problem:

Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator. Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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