Write An Equation

[nycmathguy]

Section 6.1

I need help setting up the needed equation.
I would like this problem to be done in step by step fashion. I want to learn how to put together the equation required using the information in the photo. This question ends Section 6.1 for us. Next section, Law of Cosines.

 

[MathLover1]

the angle B=180- ϕ
d/sin(θ )=2/sin(180- ϕ)
solve for d

 

[nycmathguy]

the angle B=180- ϕ
d/sin(θ )=2/sin(180- ϕ)
solve for d

d/sin(θ )=2/sin(180- ϕ)

Solve for d.

2sin(θ )= d[2/sin(180- ϕ)]

2sin(θ )/[2/sin(180- ϕ)] = d

Yes?

 

[MathLover1]

d/sin(θ )=2/sin(180- ϕ)........both sides multiply by sin(θ )

dsin(θ )/sin(θ )=2sin(θ )/sin(180- ϕ).......simplify

d=2sin(θ )/sin(180- ϕ)

 

[nycmathguy]

d/sin(θ )=2/sin(180- ϕ)........both sides multiply by sin(θ )

dsin(θ )/sin(θ )=2sin(θ )/sin(180- ϕ).......simplify

d=2sin(θ )/sin(180- ϕ)

Are you saying that I forgot to further simplify? Did I solve for d incorrectly?

 

[MathLover1]

yes, you made mistake
your solution is 2sin(θ )/[2/sin(180- ϕ)] = d which is

, when you simplify that you get

which is incorrect

correct answer is

 

[nycmathguy]

yes, you made mistake
your solution is 2sin(θ )/[2/sin(180- ϕ)] = d which is

, when you simplify that you get

which is incorrect

correct answer is

Beautiful. What does the answer look like on the xy-plane?

 

[MathLover1]

in the xy-plane, d represents y, sin function represents x

 

[nycmathguy]

in the xy-plane, d represents y, sin function represents x

Ok. I will try graphing it on paper when time allows.