ICA example 2

Request: “A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meters from the wall. What is the angle between the ladder and the ground?”

A detailed analysis by ChatGPT-o1 on the quality of the following two responses shows that Ditana Assistant’s ICA can avoid fundamental errors in the output:

• Answer 2 is correct, and it demonstrates a proper understanding and application of trigonometric functions, with all intermediate steps accurately calculated.
• Answer 1, while partially correct in its calculation, contains a fundamental error in explaining the trigonometric relationships and does not provide the final numerical value of the angle.

See public link to the comparison for the full picture.

Without ICA (default)

❯ ./ditana-assistant "A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meters from the wall. What is the angle between the ladder and the ground?"
                                    is English: "A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meter..."
                  does not refer to a computer: "A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meter..."

Here’s how to solve this problem using trigonometry: Understanding the Problem

• We have a right triangle formed by the ladder, the wall, and the ground.
• The ladder is the hypotenuse (the longest side).
• The distance from the wall to the base of the ladder is one leg.
• The angle between the ladder and the ground is what we need to find. Using Trigonometry The trigonometric function that relates the opposite side, adjacent side, and hypotenuse is the tangent (tan).
• tan(angle) = opposite / adjacent Applying the Information

1. Opposite: The ladder reaches 4 meters up the wall, so the opposite side is 4 meters.
2. Adjacent: The base of the ladder is 3 meters from the wall, so the adjacent side is 3 meters. Calculating the Angle

• tan(angle) = 4 / 3
• angle = arctan(4/3) Using a Calculator You can use a calculator to find the arctangent of 4/3. The result will be the angle in degrees. Important Note: The angle will be an acute angle (less than 90 degrees). Let me know if you’d like me to calculate the angle using a specific calculator!

With ICA

❯ ./ditana-assistant -a "A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meters from the wall. What is the angle between the ladder and the ground?"
                             is English: "A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meter..."
           does not refer to a computer: "A ladder leaning against a wall reaches 4 meters up the wall. The bottom of the ladder is 3 meter..."
                       contextual query: "What is the angle between the ladder and the ground, given the ladder's height is 4 meters and it..."
Wolfram|Alpha declined contextual query: "The input cannot be interpreted or no short answer is available."
             answer to contextual query: "Here's how to solve this problem using trigonometry:  **Understanding the Problem**  * We have a ..."

Here’s how to solve this problem:

Understanding the Problem

• We have a right triangle formed by the ladder, the ground, and the wall.
• The ladder is the hypotenuse (the longest side).
• The distance from the wall to the base of the ladder is one leg.
• The height the ladder reaches on the wall is the other leg.

Using Trigonometry

We can use the sine function to find the angle:

• sin(angle) = opposite side / hypotenuse

In our case:

• Opposite side = height of the ladder = 4 meters
• Hypotenuse = length of the ladder = unknown
• We need to find the angle (angle)

Solving for the Angle

1. Substitute the values: sin(angle) = 4 meters / hypotenuse
2. Use the Pythagorean theorem: hypotenuse² = base² + height²
   • hypotenuse² = 3 meters² + 4 meters²
   • hypotenuse² = 25 meters²
   • hypotenuse = √25 meters² = 5 meters
3. Substitute the hypotenuse back into the sine equation: sin(angle) = 4 meters / 5 meters
4. Solve for the angle: angle = arcsin(4/5)
5. Calculate the angle: angle ≈ 53.13 degrees

Answer: The angle between the ladder and the ground is approximately 53.13 degrees.

Let me know if you have any other geometry problems!