Question

Find the length of side x in simplest form with a rational denominator

Answer 1

Given:

The figure contains a right triangle.

The two angles of the triangle are 45° each.

The length of one leg is 3 units.

The length of the hypotenuse is x units.

We need to determine the value of x.

Value of x:

The value of x can be determined using the formula,

`cos \ \theta=(adj)/(hyp)`

where
`\theta=45^(\circ)`, adj = 3 and hyp = x.

Substituting these values, we get;

`cos \ 45^(\circ)=(3)/(x)`

Simplifying, we get;

`x=(3)/(cos \ 45^(\circ))`

`x=(3)/((√(2))/(2))`

`x=3 * (2)/(√(2))`

`x=(6)/(√(2))`

Thus, the value of x is
`x=(6)/(√(2))`