Answer:
12.649
Skills needed: Trigonometry
Step-by-step explanation:
1) We need to use one of the fundamentals of trigonometry, which is:
Soh Cah Toa
---> Soh = [tex]sin(\angle x) = \frac{opposite}{hypotenuse}[/tex] ([tex]sin(\angle x) [/tex] equals the side Opposite of it divided by the Hypotenuse -- sin is short for sine (pronounced as sign)
Soh = Sine Opposite Hypotenuse
---> Cah = [tex]cos(\angle x) = \frac{adjacent}{hypotenuse}[/tex] ([tex]cos(\angle x)[/tex] equals the side adjacent (not the hypotenuse) to the angle divided by the hypotenuse -- cos is short for cosine (pronounced as co-sign)
Cah = Cosine Adjacent Hypotenuse
---> Tan = [tex]tan(\angle x) = \frac{opposite}{adjacent}[/tex] ([tex]tan(\angle x) [/tex] equals the side opposite of it divided by the side (not hypotenuse) adjacent to it -- tan is short for tangent
Tan = Tangent Opposite Adjacent
2) In this case, we are solving for adjacent:
This is because [tex]\overline{BC}[/tex] is next to [tex]\angle \theta[/tex] and [tex]\overline{BC}[/tex] is not the hypotenuse ([tex]\overline{AC}[/tex] is the hypotenuse as it is opposite the right angle)
---> We are given opposite as side [tex]x[/tex] is opposite [tex]\angle \theta[/tex]
3) Let's plug it in:
[tex]\tan \angle x = \frac{opposite}{adjacent}[/tex]
[tex]\angle \theta = 31, adjacent = 7.6, opposite = \overline{BC}[/tex]
[tex]\tan 31 = \frac{7.6}{\overline{BC}}[/tex] --> Here, we should multiply both sides by [tex]\overline{BC}[/tex]
[tex]\overline{BC} * \tan 31 = 7.6[/tex] --> To get [tex]\overline{BC}[/tex] by itself, divide both sides by [tex]\tan 31[/tex]
[tex]\overline{BC} = \frac{7.6}{tan 31}[/tex]
You have to plug this into the calculator as you cannot mentally solve trig functions.
---> Plugging it into calc:[tex]\overline{BC} = \frac{7.6}{\tan 31} = 12.6485 \text{ rounded to the ten-thousandths place}[/tex]
[tex]12.6485[/tex] is rounded to the ten-thousandths, but the problem asks for 3 SF, so that would be [tex]12.649[/tex] (rounded that 85 to 9 (or 90))
