Given information:
- ABC is a right-angled triangle where angle BAC is equal to 90 degrees.
- AC equals 80 centimeters.
- AB equals 60 centimeters.

To find:
- The length of BH.

Explanation:

Step 1: Understanding the problem
- We are given a right-angled triangle ABC, where angle BAC is a right angle (90 degrees).
- The sides of the triangle are labeled as AB, BC, and AC.
- We need to find the length of BH.

Step 2: Identifying the important information
- We know the lengths of two sides of the triangle: AB = 60 cm and AC = 80 cm.
- We need to find the length of the perpendicular BH.

Step 3: Applying the Pythagorean theorem
- In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- The Pythagorean theorem states that in a right-angled triangle, AB^2 + BC^2 = AC^2.
- Since angle BAC is a right angle, BC is the height (BH) of the triangle.

Step 4: Solving the equation
- Substituting the given values, we have:
- AB^2 + BC^2 = AC^2
- (60)^2 + BC^2 = (80)^2
- 3600 + BC^2 = 6400
- BC^2 = 6400 - 3600
- BC^2 = 2800
- Taking the square root of both sides, we find:
- BC = √2800
- Simplifying the square root, we get:
- BC ≈ 52.92 cm

Step 5: Conclusion
- The length of BH, which is equal to BC, is approximately 52.92 cm.