Question

question: in △cde, the measure of ∠e = 90°, ed = 40, dc = 41, and ce = 9. what ratio represents the sine of ∠c?

Explanation:

Step1: Recall sine - definition

In a right - triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In right - triangle \(CDE\) with \(\angle E = 90^{\circ}\), for \(\angle C\), the side opposite \(\angle C\) is \(ED\) and the hypotenuse is \(DC\).

Step2: Calculate the sine ratio

The sine of \(\angle C\) is given by \(\sin C=\frac{ED}{DC}\). Given that \(ED = 40\) and \(DC = 41\), then \(\sin C=\frac{40}{41}\).

Answer:

\(\frac{40}{41}\)