Answer: z = x and ΔABD ~ ΔECD
Explanation
• The triangles are:
As cos(w°) = sin(z°), we have to remember these trigonometric functions:
[tex]\cos(x)=\frac{adjacent}{hypotenus}[/tex][tex]\sin(x)=\frac{opposite}{hypotenuse}[/tex]
where the angle used as reference is the one for which we have to search the adjacent/opposite side and the hypotenuse (longest side, opposite to the 90º angle).
We can see from the image given that the adjacent side of w° is AD, and the hypotenuse is AB:
[tex]\cos(w\degree)=\frac{AD}{AB}[/tex]
Additionally, the opposite side of zº is ED, while the hypotenuse is EC:
[tex]\sin(z\degree)=\frac{ED}{EC}[/tex]
Additionally, the ≅ sing means that is congruent and ~ is similar.
Congruent shapes have the same area, size, angles, and lengths as each other, while similar shapes must be in the same proportion and the corresponding angles are identical but do not have the same size as each other.
Our figures are similar as they do not have the same shape, thus: z = x and ΔABD ~ ΔECD.
