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