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

Explanation: We can use Law of Sines to determine x, which is written as:

`(x)/(sin(F))=(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:

`(x)/(sin(41))=(55)/(sin(90))`

Sin(90) = 1

sin (41) = 0.6560

Substituing and rearraging:

`x=(55)/(1)(0.6560)`

x = 36.08

The value of x is 36.08 units