Question

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

w=

x=

y=

Explanation:

Step1: Find \( w \)

In a kite, one diagonal is bisected by the other. So \( w = 1.6\mathrm{cm}\)

Step2: Find \( x \)

In right - triangle \( LRY \), using the property of congruent right - triangles (since in a kite, the diagonal \( LRE \) bisects the diagonal \( FY \) and the angles at \( F \) and \( Y \)).
We know that in right - triangle \( LRF \), \(\cos48^{\circ}=\frac{1.6}{3.4}\), and in right - triangle \( LRY \), \(\angle x = 48^{\circ}\) (because the diagonal \( LRE \) bisects the angles at \( F \) and \( Y \) of the kite)

Step3: Find \( y \)

In right - triangle \( LRF \), using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 3.4\mathrm{cm}\), \(a = 1.6\mathrm{cm}\), \(b = 3.0\mathrm{cm}\) (already given for one part of the vertical diagonal).
Since the vertical diagonal \( LRE \) is symmetric in the kite (the two right - triangles \( LRF \) and \( LRY \) are congruent, and the two right - triangles \( ERF \) and \( ERY \) are congruent). So \( y=3.0\mathrm{cm}\)

Answer:

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