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A security camera is set up as shown in the diagram below. Michael, who is

feet tall, is standing in its view.

Certainly, let's analyze the diagram and address any related math problems.

**Analysis of the Diagram**

The diagram presents a right-angled triangle. Here's what we can gather:

* **Right Triangle:** The triangle formed by the camera, the person, and the point directly below the camera on the ground is a right triangle.
* **Hypotenuse:** The distance from the camera to the person (39 ft) represents the hypotenuse of the triangle.
* **Vertical Side:** The height of the camera above the ground (25 ft) is the vertical side.
* **Horizontal Side (Base):** The distance from the person to the base of the building where the camera is installed (x) is the horizontal side, which we need to find.

**To Find 'x'**

We can use the Pythagorean theorem to find 'x':

* a² + b² = c²
Where:
* c is the hypotenuse
* a and b are the other two sides.

**Applying the Pythagorean Theorem**

1. Account for the person's height:
The camera is at 25 feet, and the person is 5 feet tall. The vertical distance within the right triangle is therefore 25 ft - 5 ft = 20 ft.

2. Using the new height (20 ft) and hypotenuse (39 ft), we can rewrite our equation as:
20² + x² = 39²

3. Solve for x:
400 + x² = 1521
x² = 1521 - 400
x² = 1121
x = √1121
x ≈ 33.48 ft

**Therefore, the distance 'x' from the person to the point directly below the camera is approximately 33.48 feet.**

Let me know if you'd like to explore other types of calculations or problems based on this diagram.

What is x, the horizontal distance in feet of the camera?

A. 29.91 Ft
B. 33.48 Ft
C. 30.5 ft
D. 70.7 ft

1 answer

You've correctly used the Pythagorean theorem to calculate the horizontal distance \( x \) from the person to the base of the building where the camera is installed.

To summarize your steps:

  1. Height difference considered:

    • Camera height: 25 ft
    • Person's height: 5 ft
    • Effective vertical distance: \( 25 - 5 = 20 \) ft

  2. Pythagorean theorem applied:

    • \( 20^2 + x^2 = 39^2 \)
    • \( 400 + x^2 = 1521 \)
    • \( x^2 = 1521 - 400 \)
    • \( x^2 = 1121 \)
    • \( x = \sqrt{1121} \approx 33.48 \) ft

Therefore, the correct option for the horizontal distance \( x \) is:

B. 33.48 Ft