Question

Examine the triangle below, solve for x, rounded to two decimal places.
16
45°

Answer 1

`x= 8√(2)`

Explanation:

This is a 45, 45, 90-degree triangle.

You can tell because whenever there is a 90 degree angle (right angle) and a 45-degree angle, the last angle must be 45, too, making it 45, 45, 90.

In such a triangle, the hypotenuse is equal to some number (x) times the square root of 2.

To get 16, you must eliminate that radical 2, so you have to multiply by a square root. We know that the square root of 2 times the square root of 2 is 2, so then now we only need to get a constant to multiply it by 16.

This constant would be 8.

We know this because sqrt(2) times 8(sqrt 2) gives us 2 times 8, or 16.

Now that we know what x is, we have the solution.

The legs of a 45,45,90 degree triangle are equal to the number we need to multiply the square root of 2 by to get 16, 8(sqrt 2)

That is our answer: 8(sqrt 2)