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

x/55 = tan49°

x = 55tan49°

get out your calculator

x/55 = tan 49

34.56

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.

63.27

was that right?

Yes; 63.27 was correct.

NO IT WASNT

To find the value of x in triangle DEF, we can use the trigonometric function cosine since we have the measures of angle D and the length of side DE.

First, we need to identify which sides of the triangle are adjacent and hypotenuse to angle D. In this case, side DE is the adjacent side, and side EF is the hypotenuse.

The cosine function is defined as:

cos(angle) = adjacent side / hypotenuse

Applying this formula to triangle DEF:

cos(D) = DE / EF

Now we can substitute the known values into the equation:

cos(49°) = 55 / EF

To isolate the value of EF, we need to rearrange the equation:

EF = 55 / cos(49°)

Using a calculator, we can evaluate this expression:

EF ≈ 87.52 (rounded to two decimal places)

Therefore, the value of x (EF) rounded to the nearest hundredth is approximately 87.52.