Answer:
Sid : [tied up] This is either really good or really bad.
The sum(9) of half of the first number(1/2a) and one third of the second number(+1/3b)
That is correct
If we join the points we are gonna end up with a triangle, from there by finding the centroid of the triangle we will get a point which is equidistant from all the three points given in the diagram.
Formula for Centroid:
Step ![1](https://tex.z-dn.net/?f=%201%20)
<u>Find the length of the side MN</u>
we know that
Applying the Pythagorean Theorem
![ML^{2} =NL^{2} +MN^{2}](https://tex.z-dn.net/?f=%20ML%5E%7B2%7D%20%3DNL%5E%7B2%7D%20%2BMN%5E%7B2%7D%20%20)
Solve for MN
![MN^{2}=ML^{2} -NL^{2}](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3DML%5E%7B2%7D%20-NL%5E%7B2%7D%20%20)
in this problem
![ML=25\ units\\ NL=15\ units](https://tex.z-dn.net/?f=%20ML%3D25%5C%20units%5C%5C%20NL%3D15%5C%20units%20)
Substitute in the formula above
![MN^{2}=25^{2} -15^{2}](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3D25%5E%7B2%7D%20-15%5E%7B2%7D%20%20)
![MN^{2}=400](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3D400%20%20)
![MN=20\ units](https://tex.z-dn.net/?f=%20MN%3D20%5C%20units%20%20)
Step ![2](https://tex.z-dn.net/?f=%202%20)
<u>Find the value of cos (M)</u>
we know that
in the right triangle MNL
![cos (M)=\frac{adjacent\ side\ angle\ M}{hypotenuse}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7Badjacent%5C%20side%5C%20angle%5C%20M%7D%7Bhypotenuse%7D%20%20%20)
![adjacent\ side\ angle\ M=MN=20\ units\\ hypotenuse=ML=25\ units](https://tex.z-dn.net/?f=%20adjacent%5C%20side%5C%20angle%5C%20M%3DMN%3D20%5C%20units%5C%5C%20hypotenuse%3DML%3D25%5C%20units%20)
Substitute
![cos (M)=\frac{20}{25}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7B20%7D%7B25%7D%20%20%20)
![cos (M)=\frac{4}{5}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7B4%7D%7B5%7D%20%20%20)
![cos (M)=0.8](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D0.8%20%20%20)
therefore
The answer is
The value of cos(M) is equal to ![0.8](https://tex.z-dn.net/?f=%200.8%20)
Answer:
8. X=33º
9. X=120º
10. X= 161º
Step-by-step explanation:
For all of the 3 questions, the sum of the interior angles is equal to the exterior angle.
Hope this helps! Have a great day!