Question

in the figure below, w is a point on df. what is sin(∠few) - cos(∠wed)?

Explanation:

Step1: Find the length of \(EF\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = DF = 10\) (hypotenuse), \(a=DE = 8\), and \(b = EF\).

$$EF=\sqrt{DF^{2}-DE^{2}}=\sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}=6$$

Step2: Use the co - function identity

We know that \(\angle FEW+\angle WED = 90^{\circ}\), so \(\sin(\angle FEW)=\cos(90^{\circ}-\angle FEW)=\cos(\angle WED)\)

Answer:

\(0\)