Which equation could be used to find the value of x?

Question

Triangle DEF where angle E is a right angle. DE measures x. DF measures 55. Angle D measures 49 degrees.

cos 49° = x over 55
cos 49° = 55 over x
sin 49° = x over 55
sin 49° = 55 over x

Answer 1

In triangle DEF, where angle E is a right angle, side DE (which measures x) is the side opposite angle D, and side DF (which measures 55) is the hypotenuse. To find the value of x, we can use the sine function, since sine relates the opposite side to the hypotenuse.

The equation that can be used is:

\[ \sin(49^\circ) = \frac{x}{55} \]

Therefore, the correct option is: sin 49° = x over 55.