Finda the values of r,s,t,u,v, and w. are any of the triangles 30-60-90

Answer:r = √2 units, s = √3 units, t = 2 units, u = √5 units, v = √6 units.The right triangle whose hypotenuse is t is the 30-60-90 triangle.Step-by-step explanation:The smallest right triangle has base 1, height 1 and hypotenuse r.So, applying Pythagoras Theorem , r² = 1² + 1² = 2⇒ r = √2 units(Answer)Again, in the adjacent right triangle, similarlys² = r² + 1² = 2 + 1 = 3⇒ s = √3 units (Answer)Now, in the adjacent right triangle, similarlyt² = s² + 1² = 3 + 1 = 4⇒ t = 2 units (Answer)Again, in the adjacent right triangle, similarlyu² = t² + 1² = 4 + 1 = 5⇒ u = √5 (Answer)And, in the adjacent right triangle, similarlyv² = u² + 1² = 5 + 1 = 6⇒ v = √6 (Answer)Finally, in the adjacent right triangle, similarlyw² = v² + 1² = 6 + 1 = 7⇒ w = √7 (Answer)Now, for 30-60-90 triangle the ratio of perpendicular to base is [tex]\sqrt{3}[/tex] or [tex]\frac{1}{\sqrt{3} }[/tex].Hence, the right triangle whose base is [tex]\sqrt{3}[/tex], height 1 and hypotenuse is 2 units (i.e. t) is the 30-60-90 triangle.