Math Problem Statement

À quelle hauteur (en mètres) le projecteur est-il situé? Arrondissez votre réponse à l’unité près.

À quelle hauteur (en mètres) le projecteur est-il situé? Arrondissez votre réponse à l’unité près.

Solution

To determine the height at which the projector is located, we need to calculate the height of the triangle using the given dimensions. This configuration forms a right triangle, where the line from the projector to the base represents the height.

In this triangle:

  • One side measures 15m15 \, \text{m} (hypotenuse).
  • The other side measures 8m8 \, \text{m} (base).

We can use the Pythagorean theorem to find the height (hh), since: h=c2b2h = \sqrt{c^2 - b^2} where:

  • c=15mc = 15 \, \text{m} (hypotenuse),
  • b=8mb = 8 \, \text{m} (base).

Let’s calculate hh:

h=15282=22564=16113mh = \sqrt{15^2 - 8^2} = \sqrt{225 - 64} = \sqrt{161} \approx 13 \, \text{m}

So, the height of the projector is approximately 13 meters.

Would you like further details, or do you have any questions about this calculation?

Here are some related questions for further exploration:

  1. How would the height change if the base were increased?
  2. What if the hypotenuse length was altered—how would that affect the height?
  3. How is the height calculated if both the base and hypotenuse change?
  4. Can trigonometric functions provide an alternative solution here?
  5. How does this concept apply to real-world situations involving angles and heights?

Tip: In right triangles, the Pythagorean theorem is a reliable method for determining unknown sides when two sides are known.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem

Formulas

h = √(c² - b²)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10