Question

Determine the approximate value of x.

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

Answer 1

Answer:

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 $y$ on the figure using Right-triangle Trigonometry. In a Right-triangle the longest side is called the hypotenuse (here denoted by the sides $x$ and the one valued $5$).

So we have:

$sin(60)=\frac{opposite side}{hypotenuse}= \frac{y}{5}$

so solving for $y$ gives:

$sin(60)=\frac{y}{5}\\ y=5sin(60)\\y=\frac{5\sqrt{3} }{2}$

Similarly for the other triangle we can write:

$sin(40)=\frac{y}{x}$

$sin(40)=\frac{\frac{5\sqrt{3} }{2} }{x}$

$x=\frac{\frac{5\sqrt{3} }{2} }{sin(40)}\\\\x=6.736$

So the correct option is Option (C) 6.736