Question

Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

This is the isosceles right triangle, the diagonal of a square, the thing that so upset the Pythagoreans. The two sides and diagonal of a square are in ratio
`1:1:√(2)` so we get

`u = v = 8`

We could have also gotten this using Trig:

`u = (8 √(2)) \sin 45^\circ = 8 √(2)/√(2) = 8`

`v = (8√(2))\cos 45^\circ = 8`

Or by recognizing u=v because remaining angle is 45 so this must be isosceles so

`u^2 + u^2 = (8 √(2))^2`

`2u^2 = 2 (8^2)`

`u = 8`