Answer:
A. 20/21
Step-by-step explanation:
In order to find this you must divided 16/21 by 4/5
Or 16/21 * 5/4 which is 80/84
After reducing you get 20/21
Answer:
the answer is A.
Step-by-step explanation:
Find the measures of the three angles, in radians, of the triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).
Oduvanchick [21]
Consider triangle DEF with vertices D(1,1,1), E(1,-5,2) and F(-2,2,7).
1. Find
![\overrightarrow{DE}=(1-1,-5-1,2-1)=(0,-6,1),\\ \\\overrightarrow{DF}=(-2-1,2-1,7-1)=(-3,1,6).](https://tex.z-dn.net/?f=%5Coverrightarrow%7BDE%7D%3D%281-1%2C-5-1%2C2-1%29%3D%280%2C-6%2C1%29%2C%5C%5C%20%5C%5C%5Coverrightarrow%7BDF%7D%3D%28-2-1%2C2-1%2C7-1%29%3D%28-3%2C1%2C6%29.)
Then
![\cos \angle D=\dfrac{0\cdot (-3)+(-6)\cdot 1+1\cdot 6}{\sqrt{0^2+(-6)^2+1^2}\cdot \sqrt{(-3)^2+1^2+6^2}}=\dfrac{0}{\sqrt{37} \cdot \sqrt{46} }=0.](https://tex.z-dn.net/?f=%5Ccos%20%5Cangle%20D%3D%5Cdfrac%7B0%5Ccdot%20%28-3%29%2B%28-6%29%5Ccdot%201%2B1%5Ccdot%206%7D%7B%5Csqrt%7B0%5E2%2B%28-6%29%5E2%2B1%5E2%7D%5Ccdot%20%5Csqrt%7B%28-3%29%5E2%2B1%5E2%2B6%5E2%7D%7D%3D%5Cdfrac%7B0%7D%7B%5Csqrt%7B37%7D%20%5Ccdot%20%5Csqrt%7B46%7D%20%7D%3D0.)
2. Find
![\overrightarrow{ED}=(1-1,1-(-5),1-2)=(0,6,-1),\\ \\\overrightarrow{EF}=(-2-1,2-(-5),7-2)=(-3,7,5).](https://tex.z-dn.net/?f=%5Coverrightarrow%7BED%7D%3D%281-1%2C1-%28-5%29%2C1-2%29%3D%280%2C6%2C-1%29%2C%5C%5C%20%5C%5C%5Coverrightarrow%7BEF%7D%3D%28-2-1%2C2-%28-5%29%2C7-2%29%3D%28-3%2C7%2C5%29.)
Then
![\cos \angle E=\dfrac{0\cdot (-2)+6\cdot 7+(-1)\cdot 5}{\sqrt{0^2+6^2+(-1)^2}\cdot \sqrt{(-3)^2+7^2+5^2}}=\dfrac{37}{\sqrt{37} \cdot \sqrt{83} }=\sqrt{\dfrac{37}{83}}.](https://tex.z-dn.net/?f=%5Ccos%20%5Cangle%20E%3D%5Cdfrac%7B0%5Ccdot%20%28-2%29%2B6%5Ccdot%207%2B%28-1%29%5Ccdot%205%7D%7B%5Csqrt%7B0%5E2%2B6%5E2%2B%28-1%29%5E2%7D%5Ccdot%20%5Csqrt%7B%28-3%29%5E2%2B7%5E2%2B5%5E2%7D%7D%3D%5Cdfrac%7B37%7D%7B%5Csqrt%7B37%7D%20%5Ccdot%20%5Csqrt%7B83%7D%20%7D%3D%5Csqrt%7B%5Cdfrac%7B37%7D%7B83%7D%7D.)
3. Find
![\overrightarrow{FE}=(1-(-2),-5-2,2-7)=(3,-7,-5),\\ \\\overrightarrow{FD}=(1-(-2),1-2,1-7)=(3,-1,-6).](https://tex.z-dn.net/?f=%5Coverrightarrow%7BFE%7D%3D%281-%28-2%29%2C-5-2%2C2-7%29%3D%283%2C-7%2C-5%29%2C%5C%5C%20%5C%5C%5Coverrightarrow%7BFD%7D%3D%281-%28-2%29%2C1-2%2C1-7%29%3D%283%2C-1%2C-6%29.)
Then
![\cos \angle F=\dfrac{3\cdot 3+(-7)\cdot (-1)+(-5)\cdot (-6)}{\sqrt{3^2+(-7)^2+(-5)^2}\cdot \sqrt{3^2+(-1)^2+(-6)^2}}=\dfrac{46}{\sqrt{83} \cdot \sqrt{46} }=\sqrt{\dfrac{46}{83}}.](https://tex.z-dn.net/?f=%5Ccos%20%5Cangle%20F%3D%5Cdfrac%7B3%5Ccdot%203%2B%28-7%29%5Ccdot%20%28-1%29%2B%28-5%29%5Ccdot%20%28-6%29%7D%7B%5Csqrt%7B3%5E2%2B%28-7%29%5E2%2B%28-5%29%5E2%7D%5Ccdot%20%5Csqrt%7B3%5E2%2B%28-1%29%5E2%2B%28-6%29%5E2%7D%7D%3D%5Cdfrac%7B46%7D%7B%5Csqrt%7B83%7D%20%5Ccdot%20%5Csqrt%7B46%7D%20%7D%3D%5Csqrt%7B%5Cdfrac%7B46%7D%7B83%7D%7D.)
4.
![\angle E=\arccos0=\dfrac{\pi}{2},\\ \\ \angle D=\arccos\letf(\sqrt{\dfrac{37}{83}}\right)\approx 0.27\pi,\\ \\ \angle F=\arccos\letf(\sqrt{\dfrac{46}{83}}\right)\approx 0.23\pi.](https://tex.z-dn.net/?f=%5Cangle%20E%3D%5Carccos0%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D%2C%5C%5C%20%5C%5C%0A%5Cangle%20D%3D%5Carccos%5Cletf%28%5Csqrt%7B%5Cdfrac%7B37%7D%7B83%7D%7D%5Cright%29%5Capprox%200.27%5Cpi%2C%5C%5C%20%5C%5C%0A%5Cangle%20F%3D%5Carccos%5Cletf%28%5Csqrt%7B%5Cdfrac%7B46%7D%7B83%7D%7D%5Cright%29%5Capprox%200.23%5Cpi.)
Answer:
1) Right Angle
2) Obtuse Angle
3) Acute Angle
4) Straight Angle (Straight Line)
Step-by-step explanation:
Answer: x=20
Step-by-step explanation:
The two angles provided are vertical angles.
Vertical angles are equal in measurement.
This means we can set (3x+50) and (6x-10) equal to each other and solve for x
![3x+50=6x-10](https://tex.z-dn.net/?f=3x%2B50%3D6x-10)
Add 10 to both sides
![3x+50=6x-10\\3x+50+10=6x-10+10\\3x+60=6x](https://tex.z-dn.net/?f=3x%2B50%3D6x-10%5C%5C3x%2B50%2B10%3D6x-10%2B10%5C%5C3x%2B60%3D6x)
Subtract 3x from both sides
![3x-3x+60=6x-3x\\60=3x](https://tex.z-dn.net/?f=3x-3x%2B60%3D6x-3x%5C%5C60%3D3x)
Divide both sides by 3
![\frac{60}{3} =\frac{3x}{3} \\20=x](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7B3%7D%20%3D%5Cfrac%7B3x%7D%7B3%7D%20%5C%5C20%3Dx)