HELP (05.02 LC) Which equation could be used to find the value of x? Triangle DEF where angle E is a right angle. DE measures x. DF measures 55. Angle F measures 49 degrees.
A. cos 49° = x over 55
B. cos 49° = 55 over x sin
C. 49° = x over 55 sin
D. 49° = 55 over x

Check out the attached diagram for the visual. We have DE = x as the side opposite angle F = 49 degrees and DF = 55 as the hypotenuse.

We'll use the sine rule because it is the ratio of opposite over hypotenuse

So,

sin(angle) = opposite/hypotenuse

sin(F) = DE/DF

Based on your answer choices, nothing matches entirely perfect. Though there are some bits that do match.

It looks like choice C should read sin(49) = x/55, and if so, then choice C is the answer.

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3

i got 10.28 but that rounds up to 10.3