Question

What is the length of a leg in a 45-45-90 triangle is the hypotenuse is 8

Answer 1

The length of each leg in a 45-45-90 triangle with a hypotenuse of 8 units is approximately 5.66 units.

Step-by-step explanation:

In a 45-45-90 triangle, the lengths of the two legs are equal. Let's call the length of each leg 'x'. The hypotenuse is the side opposite the right angle. In this case, the hypotenuse is given as 8 units. According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

x² + x² = 82

2x² = 64

x² = 32

x = √32

So, the length of each leg is approximately 5.66 units.

Answer 2

The legs are both of length 4√2

Step-by-step explanation:

Let the length of one of the two equal legs be x. Then, by the Pythagorean Theorem, x^2 + x^2 = 8^2, or

2x^2 = 64, or x^2 = 32 = 2(16)

Solving for x, x = 4√2. The legs are both of length 4√2.