Answer:
see explanation
Step-by-step explanation:
Using the exact values
sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]
Since the triangle is right use the sine/cosine ratios, that is
sin45° = [tex]\frac{TU}{TV}[/tex] = [tex]\frac{TU}{9\sqrt{2} }[/tex]
Multiply both sides by 9[tex]\sqrt{2}[/tex]
9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = TU, hence
TU = 9
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cos45° = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{UV}{9\sqrt{2} }[/tex]
Multiply both sides by 9 [tex]\sqrt{2}[/tex]
9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = UV, hence
UV = 9
Since TU = UV = 9 , then triangle is isosceles
and ∠T = ∠V = 45°
