Question

In ΔCDE, the measure of ∠E = 90°, DC = 37, ED = 35, and CE = 12. What is the value of the sine of ∠D to the nearest hundredth?

A) 0.52
B) 0.48
C) 0.74
D) 0.69

Answer 1

The value of the sine of ∠D in ΔCDE to the nearest hundredth is 0.32.

Step-by-step explanation:

The student has asked: What is the value of the sine of ∠D in ΔCDE to the nearest hundredth, if ∠E = 90°, DC = 37, ED = 35, and CE = 12?

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. Since ∠E is 90°, ΔCDE is a right triangle with DC as the hypotenuse.

The sine of ∠D is the length of the opposite side, which is CE, divided by the hypotenuse, which is DC. So, sin(∠D) = CE / DC = 12 / 37. Calculating this gives us 0.3243, which, when rounded to the nearest hundredth, is 0.32.