Question

Use △DEF, shown below, to answer the question that follows:

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

What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.

I would super appreciate the answer right now!!! It'd mean a lot. Thanks!

Answer 1

There are several ways to solve this, but the law of sines is probably the easiest...

Law of Sines: sina/A=sinb/B=sinc/C for any triangle...in this case we can say:

sin48/x=sin90/55

xsin90=55sin48

x=55sin48/sin90

x≈40.873 (to nearest one-thousandth, not sure which precision you needed)