Suppose a triangle has two sides of length 33 and 37 and that the angle between these two sides is 120 what is the length of the
third side of the triangle
1 answer:
Answer:
60.65
Step-by-step explanation:
The Law of Cosines can help you figure this out. Call the given sides "a" and "b" and the given angle "C". Then the third side, "c" will satisfy the relation ...
c² = a² + b² -2ab·cos(C)
= 33² +37² -2·33·37·cos(120°) = 3679
c = √3679 ≈ 60.65476 ≈ 60.65
The length of the third side is about 60.65 units.
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Answer:
(x + 7)^2 + (y + 1)^2 = 25.
Step-by-step explanation:
The center of a circle is easy to set up. According to the formula below, the formula for the circle will be (x - a)^2 + (y - b)^2 = r^2.
In this case, a = -7 and b = -1, so we have...
(x - (-7))^2 + (y - (-1))^2 = r^2
(x + 7)^2 + (y + 1)^2 = r^2
To get the radius, we need to find the distance between the center and the point on the circle. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
In this case, x2 = -4, x1 = -7, y2 = 3, and y1 = -1.
sqrt((-4 - -7)^2 + (3 - -1)^2) = sqrt((-4 + 7)^2 + (3 + 1)^2) = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = plus or minus 5.
Since distance can only be positive, the distance is 5 units, meaning that the radius is 5 units.
5^2 = 25
So, your equation should be (x + 7)^2 + (y + 1)^2 = 25.
Hope this helps!
