Question

From the adjacent figure, find the value of $\sin {45}^o$.

Answer 1

$\sin \theta =\frac{AB}{AC}$

$\sin {45}^{\circ }=\frac{AB}{AC}$

using Pythagoras theorem, we get

$A{C}^2=(AB{)}^2+(BC{)}^2$

$A{C}^2=a^2+a^2$

$Ac=\sqrt{2}a$

$\sin {45}^{\circ }=\frac{a}{\sqrt{2}a}$

$\therefore \sin {45}^{\circ }=\frac{1}{\sqrt{2}}$