Question

Calculate the exact side length of the triangle.
12√2m
a
45°
45°
b

Answer 1

The length of the hypotenuse (c) is 24m

To calculate the side lengths of the given triangle, we can use the trigonometric ratios for a 45-45-90 triangle. In such a triangle, the sides are related in the ratio 1:1:√2.

Let a be the length of one leg, b be the length of the other leg, and (c) be the length of the hypotenuse. In this case, you provided
`\(a = 12√(2) \, m\)` and (b) is also
`\(12√(2) \, m\)`. Let (c) be the hypotenuse.

Since it's a 45-45-90 triangle, the relationship is
`\(a : b : c = 1 : 1 : √(2)\).`

Therefore, c is given by
`\(c = a * √(2)\).`

Substituting the values, we get:

`\[ c = 12√(2) * √(2) = 12 * 2 = 24 \, m \]`

So, the length of the hypotenuse (c) is 24m