help please just starting trig in geometry

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°