Determine the approximate value of x.

a. 2.045
b.3.264
c.6.736
d. not enough information

Option (C) 6.736

Step-by-step explanation:

Please look at the attached modified schematic, where I have constructed a perpendicular line to the base of the triangle.

This creates two Right triangles (i.e. one angle will always be 90°). In doing so, the 80° angle is divided into 30° and 50° angles. In doing so we also then know that on the left Right-triangle the bottom left angle will be 60° since for any Triangle all three angles must add up to 180°.

(Check your self: On the left triangle we have 90° + 30° + 60° = 180° and on the right triangle we have 90° + 50° + 40° = 180°, so we are correct).

Now let us first find the value of side named on the figure using Right-triangle Trigonometry. In a Right-triangle the longest side is called the hypotenuse (here denoted by the sides and the one valued ).

So we have:

so solving for gives:

Similarly for the other triangle we can write:

So the correct option is Option (C) 6.736