Homework Help: Geometry

Posted by Amber on Tuesday, June 5, 2012 at 7:05pm.

Two forces are pushing on an object, one at 12 lbs of Force and one at 5.66 lbs of Force. The angle between them is 35° (each is 72.5 from horizontal, such that the forces make a v with the object in the center).

17. What is the total Force on the object?

18. What is the smallest angle of the triangle?

19. What is the largest angle in the triangle?

20. What is the remaining angle of the triangle?

Please help me out, thank you <3

Geometry - Reiny, Tuesday, June 5, 2012 at 7:54pm
make a sketch
complete the parallogram with the resultant as the diagonal
consider the triangle with sides 12 and 5.66 with the contained angle of 145°, with the longest side representing the resultant
let that longest side be x
by cosine law
x^2 = 12^2 + 5.66^2 - 2(12)(5.66)cos 145°
..
..
x = 16.95... (total force on object)

smallest angle is opposite the 5.66 side, call it Ų
sinŲ/5.66 = sin145/x
sinŲ = .1915...
Ų = 11.042°

largerst angle is 145°

third angle is 180- sum of the other two
= 23.96°

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