Help needed please, done Qu but need checking!

hey all, i was just hoping that you could help me with this question, i have done it but just need it checking over

Q 1. A ladder has to be manoeuvred around a T-junction in a mine between shafts of width v and w. Calculate a formula for the total length of the ladder l in terms of v, w, and θ, then Declare this as a function in Derive. For the specific shaft widths v=2.4 and w=3.1 produce a plot of the length l against a meaningful range of θ, before finding the maximum length of ladder which could be moved between the shafts. You may assume that the ladder is held horizontal at all times.

For this would you put
v=2.4 w=3.1
Then use this formula:
SIN(A)/a = SIN(B)/b = SIN(C)/c


sin90/b = sin(90 - θ)/w

w•SIN(90)/ SIN(90 - θ) = b

sin(θ)/v = sin(90)/a

a= v.sin(90)/sin(θ)

l=a+b

l = w.sin(90)/sin(90-θ) + v.sin(90)/sin(θ)

w/sin(90-θ) + v/sin(θ)

v/sin(θ) - w/sin(θ - 90)

w/cos(θ) + v/sin(θ)

l = 3.1/cos(θ) + 2.4/sin(θ)

when θ = 10

3.15 + 13.82

1697/100

16.97

when θ = 50

199/25

7.96

when θ =80

2029/100

20.29

Is this all correct? if not where have i gone wrong?

Thanks for the help