Question

Solve for the value of Y. Round to the nearest tenth ( 1 decimal place) of necessary.​

Answer 1

The value of y, the base in a right-angled triangle with a 45-degree angle, a height of
`\(3√(2)\)`, and a hypotenuse x, is approximately 4.2 (rounded to the nearest tenth).

In a right-angled triangle with a 45-degree angle, the sides are related by the properties of a 45-45-90 triangle. The ratio of the sides is
`\(1:1:√(2)\)`.

Given that the height is
`\(3√(2)\)` and the hypotenuse is (x), the base (y) can be found using the ratio:

`\[ \text{Height} : \text{Base} : \text{Hypotenuse} = 1 : 1 : √(2) \]`

So, we have:

`\[ 3√(2) : y : x = 1 : 1 : √(2) \]`

Now, solve for y:

`\[ y = 3√(2) * 1 = 3√(2) \]`

Therefore, the value of y is
`\(3√(2)\)`, rounded to the nearest tenth.