Answer:
m = 10 , n = 5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine and tangent ratio in the right triangle and the exact values
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] and tan45° = 1 , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5\sqrt{2} }{m}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
m = 5[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 5 × 2 = 10
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tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{5\sqrt{2} }[/tex] = 1 , then
n = 5[tex]\sqrt{2}[/tex]
