let S be the right triangle with sides of length 3,4, and 5 and let T be the right triangle with sides of length 6,7,and 1. suppose theta is the angle opposite the side of length 4 in S and p is the angle opposite the side of length 8 in T. Draw both of these triangles and compute sin of theta and sin of p. What do you notice? Why do you think this is true? Explain.
No TRIANGLE with sides 6, 7, and 1 exists!