The problem involves a right-angled triangle with a hypotenuse measuring 5 meters. We need to find the lengths of the other two sides, assuming their lengths are in the given ratio. Based on the diagram provided, the lengths of the other two sides are in the ratio 3:4.

Given:

• Hypotenuse $c = 5$ meters
• Ratio of the other two sides $a : b = 3 : 4$

Let's denote the sides as:

• $a = 3x$
• $b = 4x$

We know that in a right triangle: $a^2 + b^2 = c^2$ Substituting the given values: $(3x)^2 + (4x)^2 = 5^2$ $9x^2 + 16x^2 = 25$ $25x^2 = 25$ $x^2 = 1 \quad \Rightarrow \quad x = 1$

Thus, the lengths of the other two sides are:

• $a = 3x = 3 \times 1 = 3$ meters
• $b = 4x = 4 \times 1 = 4$ meters

So, the lengths of the other sides are 3 meters and 4 meters.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What is the area of this triangle?
2. How do you determine the perimeter of the triangle?
3. Can you find the sine, cosine, and tangent of one of the non-right angles in the triangle?
4. How would the side lengths change if the hypotenuse were doubled?
5. How can the Pythagorean theorem be used to verify that a triangle is a right triangle?

Tip: For any right triangle with sides in the ratio 3:4:5, the triangle is automatically a right triangle due to the Pythagorean theorem.