Question

create a poster involving a real world problem using the pythagorean theorem. the poster must include: - written description of the situation. - diagram of the situation. - all steps shown for how to solve the problem. - swag (make it look pretty and colorful)

Explanation:

Poster: Using Pythagorean Theorem to Find the Length of a Ladder Against a Wall

1. Written Description of the Situation

A painter needs to lean a ladder against a vertical wall to reach the top of the wall to paint. The base of the ladder is 6 feet away from the bottom of the wall (horizontal distance), and the wall is 8 feet tall (vertical height). We need to find the length of the ladder required to reach the top of the wall.

2. Diagram of the Situation

(You can draw a right - angled triangle where:

• The vertical side (height of the wall) is labeled as \( a = 8 \) feet.
• The horizontal side (distance from the base of the ladder to the wall) is labeled as \( b = 6 \) feet.
• The hypotenuse (length of the ladder) is labeled as \( c \), which we need to find.
• Color the wall (vertical side) blue, the ground (horizontal side) brown, and the ladder (hypotenuse) green. Add some decorative elements like a small paint bucket at the top of the ladder and some paint splatters around to make it look “SWAG” - y!)

3. Steps to Solve the Problem

The Pythagorean Theorem states that for a right - angled triangle, \( a^{2}+b^{2}=c^{2} \), where \( a \) and \( b \) are the lengths of the two legs (the sides forming the right angle) and \( c \) is the length of the hypotenuse (the side opposite the right angle).

Step 1: Identify the values of \( a \), \( b \)

We know that \( a = 8 \) feet (height of the wall) and \( b = 6 \) feet (distance from the base of the ladder to the wall).

Step 2: Substitute the values into the Pythagorean Theorem

Substitute \( a = 8 \) and \( b = 6 \) into the formula \( a^{2}+b^{2}=c^{2} \).
\( 8^{2}+6^{2}=c^{2} \)

Step 3: Calculate the squares

\( 8^{2}=64 \) and \( 6^{2}=36 \). So the equation becomes:
\( 64 + 36=c^{2} \)

Step 4: Add the numbers on the left - hand side

\( 64+36 = 100 \), so \( c^{2}=100 \)

Step 5: Solve for \( c \)

Take the square root of both sides. Since length cannot be negative, we take the positive square root.
\( c=\sqrt{100}=10 \)

4. SWAG (Make it Look Pretty and Colorful)

• Use bright colors for the triangle (e.g., red for the right angle symbol, different shades for the sides).
• Add a border around the poster with a pattern of paintbrushes and paint cans.
• Write the title “Pythagorean Theorem in Action: Ladder and Wall Problem” in a fancy, colorful font at the top.

Answer:

The length of the ladder required is 10 feet.