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Given : VU = 8 cm, let SV = n and SU = m

  • [tex] \tan(45) = \dfrac{8}{m} [/tex]

  • [tex]1 = \dfrac{8}{m} [/tex]

  • [tex]m = 8 \: \: cm[/tex]

so, SU = 8 cm

  • [tex] \sin(45) = \dfrac{8}{n} [/tex]

  • [tex] \dfrac{1}{ \sqrt{2} } = \dfrac{8}{n} [/tex]

  • [tex]n = 8 \sqrt{2} [/tex]

SV = [tex]8\sqrt{2}[/tex]

now,

The ratio of sides of Triangle SUV is :

  • [tex]8 : 8 : 8 \sqrt{2} [/tex]

  • [tex]1 :1 : \sqrt{2} [/tex]

hence, correct choice is C

In ∆SUV

  • tan45=VU/SU

So

  • VU=SU=8 as tan45=1

Rest for SV

use Pythagorean theorem

  • SV²=8²+8²
  • SV=8√2

So ratio is

  • 1:1:√2

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