Answer:
12.649
<u>Skills needed: Trigonometry</u>
Step-by-step explanation:
1) We need to use one of the fundamentals of trigonometry, which is:
Soh Cah Toa
---> Soh =
(
equals the side <u><em>O</em></u>pposite of it divided by the <u><em>H</em></u>ypotenuse -- sin is short for sine (pronounced as sign)
Soh = Sine Opposite Hypotenuse
---> Cah =
(
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 =
(
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
is next to
and
is not the hypotenuse (
is the hypotenuse as it is opposite the right angle)
<em>---> We are given </em><em>opposite </em><em>as side </em>
is opposite ![\angle \theta](https://tex.z-dn.net/?f=%5Cangle%20%5Ctheta)
3) Let's plug it in:
![\tan \angle x = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Ctan%20%5Cangle%20x%20%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%7D)
![\angle \theta = 31, adjacent = 7.6, opposite = \overline{BC}](https://tex.z-dn.net/?f=%5Cangle%20%5Ctheta%20%3D%2031%2C%20adjacent%20%3D%207.6%2C%20opposite%20%3D%20%5Coverline%7BBC%7D)
--> Here, we should multiply both sides by ![\overline{BC}](https://tex.z-dn.net/?f=%5Coverline%7BBC%7D)
--> To get
by itself, divide both sides by ![\tan 31](https://tex.z-dn.net/?f=%5Ctan%2031)
![\overline{BC} = \frac{7.6}{tan 31}](https://tex.z-dn.net/?f=%5Coverline%7BBC%7D%20%3D%20%5Cfrac%7B7.6%7D%7Btan%2031%7D)
You have to plug this into the calculator as you cannot mentally solve trig functions.
---> Plugging it into calc:![\overline{BC} = \frac{7.6}{\tan 31} = 12.6485 \text{ rounded to the ten-thousandths place}](https://tex.z-dn.net/?f=%5Coverline%7BBC%7D%20%3D%20%5Cfrac%7B7.6%7D%7B%5Ctan%2031%7D%20%3D%2012.6485%20%5Ctext%7B%20rounded%20to%20the%20ten-thousandths%20place%7D)
is rounded to the ten-thousandths, but the problem asks for 3 SF, so that would be
(rounded that 85 to 9 (or 90))