Find an equation of the circle tangent to the lines x=1, x=9, y=0
2 answers:
Answer:
Step-by-step explanation:
Given that a circle has tangents x=1, x=9 and y=0
Since two parallel lines are tangents the distance between these two lines give diameter of the circle
Distance between x=1 and x=9 is units
radius = 4 units ...i
Since y=0 is tangent, the centre will be having y coordinate as 4.
Since centre lies in the middle of x=1 and x=9 the centre will have x coordinate
as 5
Hence equation of the circle is
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Answer: Choice A. sin(A) = cos(B)
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Explanation:
The rule is that sin(A) = cos(B) if and only if A+B = 90.
Note how
- sin(A) = opposite/hypotenuse = BC/AB
- cos(B) = adjacent/hypotenuse = BC/AB
Since both result in the same fraction BC/AB, this helps us see why sin(A) = cos(B). Similarly, we can find that cos(A) = sin(B).
In the diagram below, the angles A and B are complementary, meaning they add to 90 degrees. So this trick only applies to right triangles.
The side lengths can be anything you want, as long as you're dealing with a right triangle.
