Answer:
see explanation
Step-by-step explanation:
Calculate the length of EG in the right triangle using Pythagoras' identity
EG² + 6² = 8²
EG² + 36 = 64 ( subtract 36 from both sides )
EG² = 28 ( take the square root of both sides )
EG = [tex]\sqrt{28}[/tex] = [tex]\sqrt{4(7)}[/tex] = 2[tex]\sqrt{7}[/tex]
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tanF = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{EG}{GF}[/tex] = [tex]\frac{2\sqrt{7} }{6}[/tex] = [tex]\frac{\sqrt{7} }{3}[/tex]
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sec E = [tex]\frac{1}{cosE}[/tex] and
cosE = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EG}{EF}[/tex] = [tex]\frac{2\sqrt{7} }{8}[/tex], thus
secE = [tex]\frac{1}{\frac{2\sqrt{7} }{8} }[/tex] = [tex]\frac{8}{2\sqrt{7} }[/tex] = [tex]\frac{4}{\sqrt{7} }[/tex] ← rationalise the denominator
secE = [tex]\frac{4}{\sqrt{7} }[/tex] × [tex]\frac{\sqrt{7} }{\sqrt{7} }[/tex] = [tex]\frac{4\sqrt{7} }{7}[/tex]
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cosF = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{FG}{EF}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
