Answer:
see explanation
Step-by-step explanation:
Using the cosine and tangent trigonometric ratios and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{m}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] × m = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )
m = [tex]\frac{12}{\sqrt{3} }[/tex] ← rationalise by multiplying numerator/ denominator by [tex]\sqrt{3}[/tex] )
m = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{12\sqrt{3} }{3}[/tex] = 4[tex]\sqrt{3}[/tex]
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tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{6}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] × n = 6 ( divide both sides by [tex]\sqrt{3}[/tex] )
n = [tex]\frac{6}{\sqrt{3} }[/tex] ← rationalise the denominator
n = [tex]\frac{6}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]
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