Answer:
50
110
90
=250
Step-by-step explanation: 90+50+110
I HOPE THIS HELPS
Answer: 1, 6/1, 1/1
Step-by-step explanation:
ANSWER
The length of a Diameter is 3.714
EXPLANATION
The circumscribed triangle is shown in the attachment.
We use the cosine ratio to find the altitude of the isosceles triangle.
![\cos(60 \degree) = \frac{altitude}{hypotenuse}](https://tex.z-dn.net/?f=%20%5Ccos%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Baltitude%7D%7Bhypotenuse%7D%20)
![\cos(60 \degree) = \frac{altitude}{8}](https://tex.z-dn.net/?f=%20%5Ccos%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Baltitude%7D%7B8%7D%20)
Altitude =8cos(60°)
Altitude=4cm
Let the upper half of the altitude be y cm.
Then the radius of the circle is (y-4)cm
The upper radius meets the tangent at right angles.
From the smaller right triangle,
![\sin(60 \degree) = \frac{4 - y}{y}](https://tex.z-dn.net/?f=%20%5Csin%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7B4%20-%20y%7D%7By%7D%20)
![y\sin(60 \degree) = 4 - y](https://tex.z-dn.net/?f=%20y%5Csin%2860%20%5Cdegree%29%20%20%3D%204%20-%20y)
![y\sin(60 \degree) + y= 4](https://tex.z-dn.net/?f=y%5Csin%2860%20%5Cdegree%29%20%20%20%2B%20y%3D%204%20)
![(\sin(60 \degree) + 1)y= 4](https://tex.z-dn.net/?f=%28%5Csin%2860%20%5Cdegree%29%20%20%20%2B%201%29y%3D%204%20)
![y= \frac{4}{\sin(60 \degree) + 1}](https://tex.z-dn.net/?f=y%3D%20%20%5Cfrac%7B4%7D%7B%5Csin%2860%20%5Cdegree%29%20%20%20%2B%201%7D%20)
![y = 16 - 8 \sqrt{3}](https://tex.z-dn.net/?f=y%20%3D%2016%20-%208%20%5Csqrt%7B3%7D%20)
y=1.857
The diameter is 2y
![d = 32 - 16 \sqrt{3}](https://tex.z-dn.net/?f=d%20%3D%2032%20-%2016%20%5Csqrt%7B3%7D%20)
=2(1.875)
The length of a Diameter is 3.714
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