Maths....2 unknowns?

Question

This is from an engineering statics question but I thought it maths relevant.....I just can't work out F1 or θ because there are 2 unknowns here.

Resultant Force X =

F1cosθ = 800sin60 - 166.15

F1cosθ = 526.67

Resultant force Y =

F1sinθ = 200 + 69.23 + 800cos60

F1sinθ = 669.23

Any help is much appreciated.....cheers :-)

Answer 1

Divide the two expressions you have! :

F1 cosθ / F1sinθ = 526.67/669.23

Put it upside down:

sinθ / cosθ = tanθ=669.23/526.67

From the tanθ you'll get θ and then use any of the two equations to obtain the value of F1.

θ = 51.8º

Then F1 = 851.6 N

Answer 2

Solve both equations for F1:

F1cosθ = 526.67

F1 = 526.67/cosθ

F1sinθ = 669.23

F1 = 669.23/sinθ

Known identity:

sinθ/cosθ = tanθ

526.67/cosθ = 669.23/sinθ

sinθ/cosθ = 669.23/526.67

tanθ = 1.27



θ = 51.8 degrees

Use one of the original equations to solve for F1:

F1cosθ = 526.67

F1 = 526.67/cosθ

F1 = 526.67/cos(51.8)

F1 = 526.67/.6184

F1 = 851.7 Newtons

Let's check using the other equation:

F1sinθ = 669.23

F1 = 669.23/sinθ

F1 = 669.23/sin(51.8)

F1 = 669.23/.7859

F1 = 851.5 Newtons

The two answers are very close, so it's likely the difference between the two is likely due to carrying the interim steps to too many decimal places. Maybe the value for θ should be rounded to 52 degrees, then recalculate the value of F1. But the answers are very close.

Answer 3

i think u can solve it like this:

( don't have the "theta" so x is the unknown angle)

F1cosx = 526.67

F1 ( 1 - sin^2x ) ^1/2 = 526.67

squaring both sides

F1^2  - (F1 sinx)^2 = 526.67^2

substituting F1 sin x = 669.23

in the above equation

F1^2 = 277381.3 + 669.23^2

F1^2 = 725250.1

F1 = 851.61

cos x = 526.67/F1

x = 51.79

answer may depend on the number of significant figurres used.