MHB Help Solving Questions | Get Professional Assistance

  • Thread starter Thread starter squexy
  • Start date Start date
AI Thread Summary
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.
squexy
Messages
18
Reaction score
0

Attachments

  • aiudhuaishd.jpg
    aiudhuaishd.jpg
    7.9 KB · Views: 96
  • asdiasuid.jpg
    asdiasuid.jpg
    12 KB · Views: 91
  • Trigoasdasd.jpg
    Trigoasdasd.jpg
    19.2 KB · Views: 104
Mathematics news on Phys.org
squexy said:
https://www.physicsforums.com/attachments/2941

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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

Similar threads

Replies
3
Views
1K
Replies
1
Views
998
Replies
1
Views
1K
Replies
3
Views
1K
Replies
2
Views
2K
Replies
3
Views
2K
Replies
2
Views
995
Back
Top