1. Warmup:Solve for y

2. 8.2 Special Right Triangles
LEQ: What are special right triangles and how do we use them?

3. The “root” of it all…
Calculate the value of each hypotenuse in a triangle as a reduced radical… Do you notice a trend? Is there an easier way to calculate (shortcuts)?
(hint: label sides with numbers)

4. Side lengths of Special Right Triangles
Right triangles whose angle measures are 45°-45°-90° or 30°-60°-90° are called special right triangles.
The theorems that describe these relationships of side lengths of each of these special right triangles follow….

5. Theorem 8-5: 45°-45°-90° Triangle Theorem
In a 45°-45°-90° triangle, the hypotenuse is √2 times as long as each leg.
45°
x√2
45°
Hypotenuse = leg ∙ √2

6. Finding the hypotenuse in a 45°-45°-90° Triangle
Ex 1: Find the value of x at the right.
Ex 2: Find the length of the hypotenuse of a triangle with legs of length 5√3. x
45°
2√16

7. Finding a leg in a 45°-45°-90° Triangle
Ex. 3 Find the value of x and y. 5
45° x y

8. Theorem 8-6: 30°-60°-90° Triangle Theorem
In a 30°-60°-90° triangle:
the hypotenuse is twice as long as the shorter leg
the longer leg is √3 times as long as the shorter leg.
60°
30°
x√3
Hypotenuse = 2 ∙ (shorter leg)
Longer leg = (shorter leg) ∙ √3

9. Alternatives? OF COURSE!!
If you don’t care for shortcuts, you may memorize… 60 2 45 1 √2 1 30 √3 45 1

10. Finding side lengths in a 30°-60°-90° Triangle
Ex. 1 Find the values of s and t and the right.
Ex. 2 Find the value of each variable.
60°
30°
60° 8 x
30° y

11. Real World Connection
The yield sign is an equilateral triangle. It has a height of 18√3.
Find x and y.
y inch.
18√3
x inch.