Question

the figure below is a kite. solve for w, x, and y

w = 1.6
x = 48
y =

Explanation:

Step1: Use the property of kite's diagonals

In a kite, one diagonal is the perpendicular bisector of the other. So, \( w = 1.6\) cm (the non - main diagonal is bisected). And \(x = 48^{\circ}\) (the angles between unequal sides and the bisecting diagonal are equal).

Step2: Use Pythagorean theorem for \(y\)

In the right - triangle formed by half of the non - main diagonal (\(1.6\) cm), the part of the main diagonal (\(3.0\) cm), and the side of the kite (\(3.4\) cm). For the lower right - triangle (using Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), here \(c = 3.4\) cm, \(a = 1.6\) cm, and we want to find \(b\) (the other part of the main diagonal which is \(y\)). But we can also note that in a kite, the two right - triangles (formed by the diagonals) on the lower part are congruent. Since the upper right - triangle has sides \(1.6\) cm (half of non - main diagonal) and \(3.0\) cm (part of main diagonal) and hypotenuse \(3.4\) cm (\(1.6^{2}+3.0^{2}=2.56 + 9=11.56=3.4^{2}\)), the lower right - triangle (with half of non - main diagonal \(1.6\) cm and we need to find \(y\)) also satisfies the Pythagorean theorem. Let's use the property of congruent right - triangles (formed by the diagonals of the kite). The two right - triangles above \(R\) and below \(R\) (with respect to the non - main diagonal) are congruent. So \(y = 3.0\) cm.

Answer:

\(w = 1.6\) cm, \(x = 48^{\circ}\), \(y = 3.0\) cm