This looks like a set of problems asking to find the six trigonometric functions for several right triangles, as well as to solve for the missing sides in some cases. I'll go through each of the problems one by one.

Problem 1:

For the triangle with sides 24, 25, and 7, we need to find the six trigonometric functions:

• Sine (sin) = opposite/hypotenuse
• Cosine (cos) = adjacent/hypotenuse
• Tangent (tan) = opposite/adjacent
• Cosecant (csc) = 1/sine
• Secant (sec) = 1/cosine
• Cotangent (cot) = 1/tangent

We can apply these definitions once the sides are identified.

Problem 2:

For the triangle with sides 9, 12, and 15, we can similarly find the six trigonometric functions.

Problem 3:

For the triangle with sides 5, 5√2, and 5, we apply the same steps as above to find the trigonometric ratios.

Problem 4:

For the triangle with sides 4√34, 12, and 8, we'll use the same method to determine the six functions.

Problem 5:

For the triangle with sides 8 and 12, we'll need to calculate the third side using the Pythagorean theorem, and then find the six trigonometric functions.

Problem 6:

For the triangle with sides 7 and 13, we need to find the third side (again using the Pythagorean theorem) and then proceed with the trigonometric functions.

Let me start by solving each problem step by step. Would you like me to explain the process in detail as I go, or would you prefer just the final answers for the trigonometric functions?