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175/x = tan30° x = ?

 

and 

 

tan(x) = 1/12

Guest Feb 10, 2017
edited by Guest  Feb 10, 2017
 #1
avatar+7266 
+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 = \(175\sqrt{3}\)

-------------------------------------------------

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
edited by hectictar  Feb 11, 2017

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