Sound attenuation barrier height (trigonometry)

[jhmz]

Homework Statement

http://img543.imageshack.us/img543/4598/photosfr.jpg

Find dss, dsr and thus hs.

Homework Equations

trig

The Attempt at a Solution

dss = hs/(sin[θ])
dsr = hs/(sin[∅])

dss = 3.059/(cos[θ])
dsr = 47.191/(cos[∅])

θ = arctan(hs/3.059)
∅ = arctan(hs/47.191)

I have tried many times to solve this; usually by substituting the last two equations into the first 4 and trying to solve but without success.

The problem is to do with ISO9613 where Z (path difference between dss+dsr and d) = 7.81 m and d = 50.25 m.

http://www.cevreselgurultu.cevreorm...ps/assessment_methods/industry_ISO_9613-2.pdf (page 21-25)

 

[DrOnline]

http://img543.imageshack.us/img543/4598/photosfr.jpg

OP's image.

 

[haruspex]

Let d comprise d₁ (dss side) and d₂. Write D = dss+dsr.
D = √(d₁²+h²) + √(d₂²+h²)
D² = d₁²+2h²+d₂²+2√((d₁²+h²)(d₂²+h²))
D² - d₁²-2h²-d₂²=2√((d₁²+h²)(d₂²+h²))
Squaring again leaves a quadratic in h².