Analytic Geometry A
2 - Right Triangle Trigonometry
Day 24 – Notes
Name: ________________________________________________ Date: _______________________
45°-45°-90° Triangles
Pythagorean Theorem = a2 + b2 = c2
Use the Pythagorean Theorem to find the hypotenuse for each of the following
triangles. Leave your answer in radical form.
Do you notice a pattern?
Here is the algebra behind what you just discovered.
45-45-90 Corollary: If a triangle is an isosceles right triangle, then its sides are in the
extended ratio x : x : x 2 .
Now, let’s use this ratio to solve for either the hypotenuse of a 45°-45°-90° triangle or the
missing sides of a 45°-45°-90° triangle.
Example 1:
Find the length of the missing leg and the hypotenuse.
Use the x : x : x 2 ratio to label your triangle.
x 2
x
x
substitute 6 in for x
x
6 2
x6
Analytic Geometry A
2 - Right Triangle Trigonometry
Day 24 – Notes
Your turn! Find the missing leg and the hypotenuse.
a)
b)
Example 2:
Find the length of both missing legs.
Again, use the x : x : x 2 ratio to label your triangle.
x
x 2
After doing so, you can see that we need to solve for x, which will give use the length of
both legs.
The Ti-36 Pro will rationalize this for you
16
by typing in
and hitting “enter”.
2
Your turn! Find the missing legs.
a)
b)