Question

Find the remaining side of a 45° – 45° – 90° triangle if the shorter sides are 2/3 each .

Answer 1

Answer:

The length of the longer side is 2√2/3

Step-by-step explanation:

A 45-45-90 triangle is a right-angled triangle.

In fact, since it has two angles equal, it is a right angled isosceles triangle. What we are saying is that two of its sides are equal.

Hence, we have two short sides which are the opposite and the adjacent and a longer side which is the hypotenuse

Thus, to find the length of the longer side, we employ Pythagoras’ theorem and it states that the square of the hypotenuse equals the sum of the squares of the two other sides;

Mathematically, let’s call the longer side x

so x^2 = (2/3)^2 + (2/3)^2

x^2 = 4/9 + 4/9

x^2 = 8/9

x = √(8/9)

x = 2√2/3