The image presents a geometry problem involving two buildings and a right triangle formed between them. Let's analyze the situation step by step.
---
Given:
- Height of the
left building = 32 meters.
- Height of the
right building = 41 meters.
- The horizontal distance between the two buildings = 12 meters (marked as AB).
- We are to find the
height difference between the top of the taller building and the top of the shorter one, and possibly the length of the line connecting the tops (hypotenuse), based on the triangle shown.
---
Step 1: Understand the Geometry
Let’s label the points:
- Point
A: Top of the shorter building (32 m high).
- Point
B: Base of the taller building (same level as A horizontally).
- Point
C: Top of the taller building (41 m high).
So, the vertical difference between the tops is:
$$
41\,\text{m} - 32\,\text{m} = 9\,\text{m}
$$
This gives us a
right triangle ABC, where:
-
AB = 12 m (horizontal leg),
-
BC = 9 m (vertical leg),
-
AC is the hypotenuse — the line from the top of the shorter building to the top of the taller one.
---
Step 2: Use the Pythagorean Theorem
We want to find the length of
AC, the hypotenuse:
$$
AC^2 = AB^2 + BC^2
$$
$$
AC^2 = 12^2 + 9^2 = 144 + 81 = 225
$$
$$
AC = \sqrt{225} = 15\,\text{m}
$$
---
✔ Answer:
The distance from the top of the shorter building to the top of the taller building (the hypotenuse) is
15 meters.
---
Explanation Summary:
- The height difference between the buildings is 9 meters.
- The horizontal distance is 12 meters.
- Using the Pythagorean theorem: $ \sqrt{12^2 + 9^2} = \sqrt{225} = 15 $.
- So, the straight-line distance between the tops is
15 meters.
This is a classic application of the
Pythagorean Theorem in real-world contexts like architecture or surveying.
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem in real life.
