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 $1:1:\sqrt{2}$ so we get

$u = v = 8$

We could have also gotten this using Trig:

$u = (8 \sqrt{2}) \sin 45^\circ = 8 \sqrt{2}/\sqrt{2} = 8$

$v = (8\sqrt{2})\cos 45^\circ = 8$

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

$u^2 + u^2 = (8 \sqrt{2})^2$

$2u^2 = 2 (8^2)$

$u = 8$