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,

$cos \ \theta=\frac{adj}{hyp}$

where $\theta=45^{\circ}$, adj = 3 and hyp = x.

Substituting these values, we get;

$cos \ 45^{\circ}=\frac{3}{x}$

Simplifying, we get;

$x=\frac{3}{cos \ 45^{\circ}}$

$x=\frac{3}{\frac{\sqrt{2}}{2}}$

$x=3 \times \frac{2}{\sqrt{2}}$

$x=\frac{6}{\sqrt{2}}$

Thus, the value of x is $x=\frac{6}{\sqrt{2}}$