The discussion focuses on solving a trigonometry puzzle related to a chord of 70 km on a circle representing the Earth. Participants emphasize the importance of drawing a diagram that includes the Earth's radius and the chord, utilizing right triangles to find the unknown lengths. The Pythagorean theorem is identified as a key tool for determining the length of the radius segment above the chord. The conversation highlights the necessity of visual aids in tackling geometry problems effectively.
PREREQUISITESStudents, educators, and anyone interested in enhancing their problem-solving skills in trigonometry and geometry, particularly in relation to real-world applications.
Draw a diagram involving the circle representing the Earth, two conveniently chosen radii, and the chord of interest.slipF said:
So you've drawn a diagram ? Which particular radii did you use ? (Look for right-triangles).slipF said:sorry, I don't know where to take it from there
Yep. But note that the radius that bisects your 70km chord has two parts, the part above the chord is the length you're looking for. You can find this part by finding the length of the part underneath the chord. My plan would be to draw another radius to connect to one endpoint of the chord. This creates a right triangle created from that radius, the unknown length of the other radius that lies between the chord and the center of the Earth, and half the chord. A diagram is always useful in solving geometry problems.slipF said: