Short Answer 
To find the adjacent side of a right triangle with a 25° angle and an opposite side of 12 units, use the tangent function: tan(25°) = 12/x. Rearranging gives x = 12/tan(25°), which can be calculated using a calculator for the final result.
Step 1: Identify the Right Triangle
Begin by recognizing that you are working with a right triangle. In this case, you are given a specific angle of 25°. For right triangles, the angles and sides have key relationships dictated by trigonometric functions. Determine the sides involved:
- Opposite side: 12 units
- Angle: 25°
- Adjacent side: unknown (this is what we will calculate)
Step 2: Use the Tangent Function
The tangent function relates the angle to the opposite and adjacent sides of a right triangle. The formula to use is:
- tan(θ) = opposite/adjacent
- For your triangle: tan(25°) = 12/x
This means you can set up the equation based on the behavior of the tangent function using the provided measurements.
Step 3: Solve for x
To find the value of x (the adjacent side), rearrange the equation to isolate x. This can be done by multiplying both sides by x and rearranging the terms:
- From tan(25°) = 12/x, multiply both sides by x: x * tan(25°) = 12
- Now, divide both sides by tan(25°): x = 12/tan(25°)
The final expression shows how you can calculate x using the known opposite side and the angle. Use a calculator to find the value of x for your specific calculations.