Question

Use DEF shown below to answer the question that follows: what is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.

Answer 1

DEF is shown in the attachment.

Answer: x = 36.08

Step-by-step explanation: We can use Law of Sines to determine x, which is written as:

$\frac{x}{sin(F)}=\frac{55}{sin(90)}$

where

F is the angle at vertex F

The angle is calculated knowing that the sum of all internal angles of a triangle is 180°:

F + 49 + 90 = 180

F + 139 = 180

F = 180 - 139

F = 41

Then, Law of Sines will be:

$\frac{x}{sin(41)}=\frac{55}{sin(90)}$

Sin(90) = 1

sin (41) = 0.6560

Substituing and rearraging:

$x=\frac{55}{1}(0.6560)$

x = 36.08

The value of x is 36.08 units