Question

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

Answer 1

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.

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, similarly

s² = r² + 1² = 2 + 1 = 3

⇒ s = √3 units (Answer)

Now, in the adjacent right triangle, similarly

t² = s² + 1² = 3 + 1 = 4

⇒ t = 2 units (Answer)

Again, in the adjacent right triangle, similarly

u² = t² + 1² = 4 + 1 = 5

⇒ u = √5 (Answer)

And, in the adjacent right triangle, similarly

v² = u² + 1² = 5 + 1 = 6

⇒ v = √6 (Answer)Finally, in the adjacent right triangle, similarly

w² = v² + 1² = 6 + 1 = 7

⇒ w = √7 (Answer)

Now, for 30-60-90 triangle the ratio of perpendicular to base is
`√(3)` or
`(1)/(√(3) )`.

Hence, the right triangle whose base is
`√(3)`, height 1 and hypotenuse is 2 units (i.e. t) is the 30-60-90 triangle.