## Trigonometry (10th Edition)

$\tan$ 45$^{\circ}$ = 1
$\tan$ 45$^{\circ}$ We must find side x of the 45$^{\circ}$ - 45$^{\circ}$ Right Triangle. Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$ x$^{2}$ = 1$^{2}$ + 1$^{2}$ x$^{2}$ = 2 x = $\sqrt2$ Now consider the triangle from the perspective of a 45$^{\circ}$ angle. Hypotenuse = $\sqrt2$ Opposite = 1 Adjacent = 1 $\tan$ 45$^{\circ}$ = $\frac{Opposite}{Adjacent}$ = $\frac{1}{1}$ = 1 Therefore: $\tan$ 45$^{\circ}$ = 1