You should know the relationship between the lengths of the sides in
two special triangles:
$\,30^\circ\text{}60^\circ\text{}90^\circ\,$ TRIANGLE

Lengths of Sides in a
$\,30^\circ\text{}60^\circ\text{}90^\circ\,$ Triangle
Let
$\,s\,$ denote the length of the shortest side.
Then, the hypotenuse has length
$\,2s\,$.
The side opposite the
$\,60^\circ\,$ angle has length
$\,\sqrt{3}s\,$.
Conversely, if a triangle has sides of lengths
$\,s\,$,
$\,\sqrt{3}s\,$, and
$\,2s\,$,
then it is a $\,30^\circ\text{}60^\circ\text{}90^\circ\,$ triangle.
Since
$\,\sqrt{3}\approx 1.7\,$,
it follows that the side opposite the $\,60^\circ\,$ angle is a little
more than one and a half times the shortest side.

$\,45^\circ\text{}45^\circ\text{}90^\circ\,$ TRIANGLE

Lengths of Sides in a $\,45^\circ\text{}45^\circ\text{}90^\circ\,$ Triangle
Let $\,s\,$ denote the length of the two shorter sides.
Then, the hypotenuse has length
$\,\sqrt{2}s\,$.
Conversely, if a triangle has sides of lengths
$\,s\,$,
$\,s\,$, and
$\,\sqrt{2}s\,$,
then it is a $\,45^\circ\text{}45^\circ\text{}90^\circ\,$ triangle.
Since
$\,\sqrt{2}\approx 1.4\,$,
it follows that the hypotenuse is a little
less than one and a half times the shortest side.

It's easy to see that these are the correct relationships between the lengths of the sides,
as follows:
$\,30^\circ\text{}60^\circ\text{}90^\circ\,$ Triangle Relationships
Start with an equiangular (hence equilateral) triangle,
where each side has length $\,2\,$.
Notice that all the angles must
be
$\,\frac{180^\circ}{3} = 60^\circ\,$.
Drop a perpendicular, as shown below.
The purple and green triangles are $\,30^\circ\text{}60^\circ\text{}90^\circ\,$ triangles,
where the length of the shortest side is $\,1\,$.
A quick application of the Pythagorean Theorem shows that the remaining side has length
$\,\sqrt{3}\,$.
Then, scale all sides by
$\,s\,$.
$\,45^\circ\text{}45^\circ\text{}90^\circ\,$ Triangle Relationships
Create a triangle with two sides of length $\,1\,$ and a $\,90^\circ\,$ angle,
as shown below.
Since angles opposite equal sides must be equal,
and since the two remaining angles must add to $\,90^\circ\,$,
they must each be $\,45^\circ\,$.
A quick application of the Pythagorean Theorem shows that the remaining side must equal
$\,\sqrt{2}\,$.
Then, scale all sides by
$\,s\,$.
EXAMPLES:
Question:
In a $\,30^{\circ}\text{}60^{\circ}\text{}90^{\circ}\,$ triangle,
suppose that the length of the hypotenuse is $\,70\,$.
What is the length of the side opposite the $\,60^{\circ}\,$ angle?
Solution:
One strategy is to get the shortest side first, which is half the hypotenuse:
the shortest side is $\,\frac{70}2 = 35\,$.
Then, the side opposite the $\,60^{\circ}\,$ angle is $\,\sqrt{3}\,$ times as long,
hence is $\,35\sqrt 3\,$.
Question:
Suppose that the lengths of the sides in a triangle are $\,13\,$, $\,13\sqrt{2}\,$, and $\,13\,$.
What type of triangle is this?
Solution:
This is a recognition question.
Notice that two sides are the same, and the other is $\,\sqrt{2}\,$ times as large.
This is a $\,45^{\circ}\text{}45^{\circ}\text{}90^{\circ}\,$ triangle.