Question

type the correct answer in the box. round your answer to two decimal places.
find the length of \\( \overline { s t } \\) in this kite.

\\( s t = \\) units

Explanation:

Step1: Use the sine function

In a right - angled triangle (formed by the properties of a kite, the diagonals are perpendicular), if we consider the triangle \( \triangle STR\), and we know the hypotenuse \(SR = 3.3\) and the angle \( \angle SRT=23^{\circ}\). The sine function is defined as \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 23^{\circ}\), the opposite side to the angle \( \theta\) is \(ST\), and the hypotenuse is \(SR\). So, \( \sin(23^{\circ})=\frac{ST}{SR}\).

Step2: Solve for \(ST\)

Since \(SR = 3.3\), we can rewrite the formula as \(ST=SR\times\sin(23^{\circ})\). We know that \( \sin(23^{\circ})\approx0.3907\). Then \(ST = 3.3\times0.3907\).

$$ST=3.3\times0.3907 = 1.29$$

Answer:

\(1.29\)