Answer and Step-by-step explanation:
To find the length of the third side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's break it down step by step:
1. Identify the sides of the right triangle.
- The two sides that are perpendicular to each other (forming the right angle) are given as 3.20m and 6.90m.
2. Apply the Pythagorean theorem.
- Let's assume the length of the third side, the hypotenuse, is 'x' meters.
- According to the Pythagorean theorem, we have the equation: 3.20^2 + 6.90^2 = x^2.
3. Calculate the length of the third side.
- Evaluating the equation: 10.24 + 47.61 = x^2.
- Adding the values: 57.85 = x^2.
- To find 'x', we need to take the square root of both sides: √57.85 = √x^2.
- Simplifying: 7.61 ≈ x.
The length of the third side of the right triangle is approximately 7.61 meters.