Geometry: 45º 45º 90º Special Triangles

45 45 90 triangle

Greetings math folks! In this post we are going to go over 45º 45º 90º special triangles and how to find the missing sides when given only one of its lengths. For even more examples, check out the video below and happy calculating! 🙂

Why is it “special”?

 The 45º 45º 90º triangle is special because it is an isosceles triangle, meaning it has two equal sides (marked in blue below).  If we know that the triangle has two equal lengths, we can find the value of the hypotenuse by using the Pythagorean Theorem.  Check it out below!

45 45 90 triangle

Now we can re-label our triangle, knowing the length of the hypotenuse in relation to the two equal legs. This creates a ratio that applies to all 45º 45º 90º triangles!

45 45 90 triangle

How do I use this ratio?

45 45 90 triangle

Knowing the above ratio, allows us to find any length of a 45º 45º 90º triangle, when given the value of one of its sides.

Let’s try an example:

45 45 90 triangle
45 45 90 triangle sides
45 45 90 triangle sides
45 45 90 triangle sides
45 45 90 triangle sides
45 45 90 triangle sides

Now let’s look at an example where we are given the length of the hypotenuse and need to find the values of the other two missing sides.

45 45 90 triangle sides
45 45 90 triangle formula
45 45 90 triangle formula
45 45 90 triangle formula
45 45 90 triangle formula
45 45 90 triangle formula
45 45 90 triangle formula

Now try mastering the art of the 45º 45º 90º special triangle on your own!

Practice Questions: Find the value of the missing sides.

45 45 90 triangle formula
45 45 90 triangle formula

Solutions:

45 45 90 triangle formula

Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! 🙂

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