Question

Find the value of x.

A. 4

B. 8√2/2

C. 4√2

D. 8√2

Answer 1

D. 8√2

Explanation:

In a 45-45-90 triangle, the two legs are congruent, and the hypotenuse is equal to √2 times the length of each leg. Let's denote the length of one leg as "a". Given that one side is 8, we can conclude that both legs of the triangle have a length of 8.

Using the formula, the hypotenuse (x) can be calculated as:

x = √2 * a

Plugging in the value of a as 8:

x = √2 * 8

x = 8√2

Therefore, the value of x (the hypotenuse) in the 45-45-90 triangle with one side measuring 8 units is 8√2.

Answer 2

D

Explanation:

using the cosine ratio in the right triangle and the exact value

cos45° =
`(1)/(√(2) )` , then using the 45° angle on the left

cos45° =
`(adjacent)/(hypotenuse)` =
`(8)/(x)` =
`(1)/(√(2) )` ( cross- multiply )

x = 8
`√(2)`