You reflect point A over the x-axis, double the distance from point a to the x-axis, then give the coordinates.
ex/ point A to the x-axis: 6, reflection: 12. coordinates (-6, 5)
Answer:
1.90
Step-by-step explanation:
I hope I helped you!
1. Since we have <span>two sides (AC and AB) and the included angle (60°), we are going to use the law of cosines to find the length of BC:
</span>
![BC= \sqrt{AB^2+AC^2-2(AB)(AC)Cos \alpha }](https://tex.z-dn.net/?f=BC%3D%20%5Csqrt%7BAB%5E2%2BAC%5E2-2%28AB%29%28AC%29Cos%20%5Calpha%20%7D%20)
![BC= \sqrt{6^2+4^2-2(6)(4)Cos(60)}](https://tex.z-dn.net/?f=BC%3D%20%5Csqrt%7B6%5E2%2B4%5E2-2%286%29%284%29Cos%2860%29%7D%20)
![BC= \sqrt{36+16-48Cos(60)}](https://tex.z-dn.net/?f=BC%3D%20%5Csqrt%7B36%2B16-48Cos%2860%29%7D%20)
![BC= \sqrt{52-48Cos(60)}](https://tex.z-dn.net/?f=BC%3D%20%5Csqrt%7B52-48Cos%2860%29%7D%20)
![BC=2 \sqrt{7}](https://tex.z-dn.net/?f=BC%3D2%20%5Csqrt%7B7%7D%20)
<span>
We can conclude that the length of the side BC is </span>
![2 \sqrt{7}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B7%7D%20)
.
2. To find the area of triangle ABC we are going to use Heron's formula:
where
![A](https://tex.z-dn.net/?f=A)
is the area of the triangle
![S](https://tex.z-dn.net/?f=S)
is the semi-perimeter of the triangle
But first, we are going to find the semi-perimeter of our triangle using the formula:
![S= \frac{A+B+C}{2}](https://tex.z-dn.net/?f=S%3D%20%5Cfrac%7BA%2BB%2BC%7D%7B2%7D%20)
We can infer for our triangle and from our previous calculation that
![A=2 \sqrt{7}](https://tex.z-dn.net/?f=A%3D2%20%5Csqrt%7B7%7D%20)
,
![B=4](https://tex.z-dn.net/?f=B%3D4)
, and
![C=6](https://tex.z-dn.net/?f=C%3D6)
. Lets replace those values to find the semi-perimeter of our triangle:
![S= \frac{A+B+C}{2}](https://tex.z-dn.net/?f=S%3D%20%5Cfrac%7BA%2BB%2BC%7D%7B2%7D%20)
![S= \frac{2 \sqrt{7+4+6} }{2}](https://tex.z-dn.net/?f=S%3D%20%5Cfrac%7B2%20%5Csqrt%7B7%2B4%2B6%7D%20%7D%7B2%7D%20)
![S=7.65](https://tex.z-dn.net/?f=S%3D7.65)
Finally, we can use Heron's formula to find the area of our triangle:
![A= \sqrt{7.65(7.65-2 \sqrt{7})(7.65-4)(7.65-6)}](https://tex.z-dn.net/?f=A%3D%20%5Csqrt%7B7.65%287.65-2%20%5Csqrt%7B7%7D%29%287.65-4%29%287.65-6%29%7D)
![A=10.42](https://tex.z-dn.net/?f=A%3D10.42)
We can conclude that the area of our triangle is
10.42 square units.