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The discussion revolves around solving mathematical problems involving trigonometry and geometry. Participants provide answers to specific questions, including the calculation of sine using the Pythagorean theorem and estimations based on coordinate geometry. There is a focus on deriving equations for lines and normals related to circles. Some responses seek clarification on the variables used in the problems, indicating confusion over the representation of triangle sides. Overall, the conversation emphasizes collaborative problem-solving and the need for clear communication in mathematical discussions.
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squexy said:
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Answer: K

38. $$\sin M=\frac{\text{ opposite }}{\text{ hypotenuse }}=\frac{KL}{MK}$$

From the Pythogorean Theorem: $$(KL)^2+(ML)^2=(MK)^2 \Rightarrow (KL)^2=144-100=44 \Rightarrow KL=\sqrt{44}$$

Therefore, $$\sin M=\frac{\sqrt{44}}{12}$$
 
What have you tried so far?
 
Prove It said:
What have you tried so far?

37
By estimative I can find the answer, since radius is 5 coordinate units I decrease 5 from Y and add 5 to X having (7,-2) 39
a = b = c3x = 180
x = 60
 
squexy said:
37
By estimative I can find the answer, since radius is 5 coordinate units I decrease 5 from Y and add 5 to X having (7,-2) 39
a = b = c3x = 180
x = 60

For 37 I would find the equation of the line passing through your two known points. Then try to find the equation of the normal to this line through the centre of the circle (keep in mind that the gradients of perpendicular lines multiply to give -1). Once you have the equation of this normal you can find where it intersects with the circle, solving your problem.

For 39 I have no idea what you are talking about. What are a, b, c? Are you using these letters to represent the sides of the triangle. If so, how do you know the sides of the triangle are all equal in length?
 
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