Answer:
The area of the triangle is ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Step-by-step explanation:
Given:
Coordinates D (0, 0), E (1, 1)
Angle ∠DEF = 60°
△DEF is a Right triangle
To Find:
The area of the triangle
Solution:
The area of the triangle is = ![\frac{1}{2}(base \times height)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28base%20%5Ctimes%20height%29)
Here the base is Distance between D and E
calculation the distance using the distance formula, we get
DE = ![\sqrt{(0-1)^2 + (0-1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%280-1%29%5E2%20%2B%20%280-1%29%5E2%7D)
DE =![\sqrt{(-1) ^2 + (-1)^2](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1%29%20%5E2%20%2B%20%28-1%29%5E2)
DE = ![\sqrt{1+1}](https://tex.z-dn.net/?f=%5Csqrt%7B1%2B1%7D)
DE = ![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
Base = ![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
Height is DF
DF =![tan(60^{\circ}) \times DE](https://tex.z-dn.net/?f=tan%2860%5E%7B%5Ccirc%7D%29%20%5Ctimes%20DE)
DF = ![\sqrt{3} \times DE](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%5Ctimes%20DE)
DF = ![\sqrt{3} \times\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%5Ctimes%5Csqrt%7B2%7D)
Now, the area of the triangle is
= ![\frac{1}{2}({\sqrt{2})(\sqrt{3} \times \sqrt{2})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%7B%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B2%7D%29)
=![\frac{1}{2}({\sqrt{2})(\sqrt{3} \sqrt{2})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%7B%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%20%5Csqrt%7B2%7D%29)
=![\frac{1}{2}(2\sqrt{3} )](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%282%5Csqrt%7B3%7D%20%29)
=![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Answer:
Nicole is correct
Step-by-step explanation:
They need to get the 3y on one side of the equal sign and the known numbers on the other side. To do this, they must subtract the 4 from both sides.
Answer:
x=120
Step-by-step explanation:
a vertical angle is equal to each other so if angle J is 120° the so is angle K
Answer:
From the origin, move 0.5 unit to the left along the x-axis and 1 unit vertically down, and place the point.
Step-by-step explanation:
hope this helps! :}