Math Problem Statement

Jack is on top of his building 85' above the ground. He aims a laser at the neighboring building 413" across the street from him. The laser reflects off the new shiny glass of the building 10' above the ground and then hits Jack's pet turtle on the street. How far does the turtle have to travel to get safe and sound back home to Jack's building? Write the answer in terms of feet & inches.

Solution

This image depicts a problem involving a laser aimed from a building to a street and reflecting to a target (a pet turtle). The goal is to find how far the turtle needs to travel to get to safety.

Let's break this down:

  1. Information from the diagram:

    • The building's height is 85 feet.
    • The horizontal distance from the building to the turtle is 75 feet.
    • The laser travels from the building to the street, reflects, and then hits the turtle located on the street.
  2. Geometry Setup:

    • A right triangle is formed with the building height, the horizontal distance to the turtle, and the hypotenuse being the laser's path.
    • The laser reflects off a shiny surface at a neighboring building that is 10 feet tall.
    • The problem seems to be solved using proportions involving similar triangles.
  3. Calculations shown in the image:

    • The ratio 900120=445X\frac{900}{120} = \frac{445}{X} is used, where:
      • 900 and 120 represent known measurements (perhaps distances or scaled values).
      • 445 is a value related to the laser's path.
      • XX represents the unknown distance the turtle must travel.

    Solving for XX: 900120=445X\frac{900}{120} = \frac{445}{X} Cross-multiply: 900X=120×445900X = 120 \times 445 900X=53400900X = 53400 X=53400900=59.33 feetX = \frac{53400}{900} = 59.33 \text{ feet} So, the turtle must travel approximately 59 feet and 4 inches to get to safety.

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Math Problem Analysis

Mathematical Concepts

Geometry
Proportions
Similar Triangles

Formulas

Proportionality: (900/120) = (445/X)

Theorems

Similar Triangles Theorem

Suitable Grade Level

Grades 8-10