#1**+7 **

175/x = tan30°

Multiply both sides by x

175 = xtan30°

Divide both sides by tan30°

175/tan30° = x

You can simply plug this into a calculator and get that **x ≈ 303.109**

You can stop there, but if you want to you can also look at a unit circle to find the exact value of tan30º.

tan30° = sin30°/cos30°

tan30° = \(\frac{1}{2}/\frac{\sqrt{3}}{2}\)

tan30° = \(\frac{1}{2}*\frac{2}{\sqrt{3}}\)

tan30°= \(\frac{2}{2\sqrt{3}}\)

tan30°= \(\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\)

so

x = \(175/\frac{1}{\sqrt{3}}\)

x = \(175*\frac{\sqrt{3}}{1}\)

x = \(175\sqrt{3}\)

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tan(x) = 1/12

Here, all you need to do is take the arctangent of both sides.

x = arctan(1/12)

Just plug this into a calculator and you get that **x ≈ 4.764°**

hectictar
Feb 11, 2017