Question

find xy.
x
w
68°
7.5
y
write your answer as an integer or as a decimal rounded to the nearest tenth.
xy =

Explanation:

Step1: Use sine function

In right - triangle \(XWY\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 68^{\circ}\), the opposite side to \(\theta\) is \(WY = 7.5\), and the hypotenuse is \(XY\). So, \(\sin68^{\circ}=\frac{WY}{XY}\).

Step2: Solve for \(XY\)

Since \(\sin68^{\circ}=\frac{7.5}{XY}\), then \(XY=\frac{7.5}{\sin68^{\circ}}\). We know that \(\sin68^{\circ}\approx0.9272\). So, \(XY=\frac{7.5}{0.9272}\approx8.1\).

Answer:

\(8.1\)