Remember that, depending on the measures of the acute angles, there are some shortcuts that help us find the lengths of the sides.
See solution.
Practice makes perfect
In general, in a right triangle, to find the length of one side by applying the Pythagorean Theorem, we need to know the length of the other two sides.
However, when the two acute angles of the right triangle have a measure of 45^(∘) each, we say it is a special right triangle because it is an isosceles triangle, and we just need to know the length of one side to find the length of the remaining two sides.
Also, if the acute angles of the right triangle have measures of 30^(∘) and 60^(∘), it is also a special right triangle because, knowing the length of just one side, we will be able to find the length of the remaining two sides.
Therefore, it is easier to work with either of these two types of right triangles than working with a general right triangle. Keep in mind that the results obtained are derived from the Pythagorean Theorem.
