1. Warm-Up
Find x.
2x+12 =6
12x=24
√25 = x

2. Lesson 10 Right Triangles and Trigonometry
Simplifying Square Roots

3. Simplifying Square Roots
Square roots are written with a radical symbol. Radical Expression: An expression written with a radical symbol Radicand: The number or expression inside the radical symbol.
√25
Radical
Radicand

4. Ex 1) What is √36. Ex 2) Simplify the radical expressions
Ex 1) What is √36? Ex 2) Simplify the radical expressions. a) √20 b) √50 c) √24 d) √48

5. c2 = a2 + b2 c2 = (√5) 2 + (√2) 2 c2 = 5 + 2 c = √7
Ex 4) Find the length of the hypotenuse. Write your answer in radical form (Do NOT use a calculator).
c2 = a2 + b2
c2 = (√5) 2 + (√2) 2
c2 = 5 + 2
c = √7
√5 cm
√2 cm

6. Find the length of hypotenus.
√13 6

7. Class Work
P. 538 #2-12 (even) P. 539 #1-11, #20-22 P. 540 #27-45 (odd) P. 577 #11-21 (odd)

8. Special triangles 45-45-90 Triangles(Balanced Triangle)
Triangles (unbalanced Triangle)

9. Triangles
A triangle is a Right Isosceles triangle, because the base angles are congruent and the 2 legs (or sides) are congruent. In a triangle, the length of the hypotenuse is the length of a leg (or side) times √2.

10. Triangles
Leg x
Hypotenuse
x√2
Leg x
45°
45°

11. Ex 1) Each triangle is a right isosceles triangle
Ex 1) Each triangle is a right isosceles triangle. What is the value of each angle? Find the value of z.
If x = 4 and the hypotenuse = x√2
Then the
hypotenuse = 4√2 cm 45
Hypotenuse is
x√2
4 cm z
4 cm
This side is x 45
This side is x

12. Hypotenuse = leg x √2 If the Hypotenuse = 3√2 Then each leg = 3 cm
Ex 2) Find the value of y.
Hypotenuse = leg x √2
If the Hypotenuse = 3√2
Then each leg = 3 cm
Y=3 cm y
3√2 cm y

13. If the Hypotenuse = x√2 and each side is x
Ex 3) Draw a right isosceles triangle with a hypotenuse of 5cm. How do we find the length of the other 2 sides
If the Hypotenuse = x√2 and each side is x
x √2 = 5 cm
x= 5 √2
5 cm
Leg

14. 30-60-90 Triangles Long Side = Short side • √3 Short Side = Long Side
Hypotenuse = Short • 2
30°
Long Side Hypotenuse
x√ x
Short side x
60°

15. Triangles
In a Triangle, the length of the hypotenuse is twice the length of the short side (x). The long side is length of the short side times √3

16. Ex 1) Using the Pythagorean Theorem, find the missing side.
c² = a² + b²
8² = 4² + b²
64 = 16 + b²
64-16 = b²
b = √48
60°
8cm
4cm
side
30°
Long Side = x√3
b = 4√3 cm

17. Ex 2) Find the value of each variable
Ex 2) Find the value of each variable. Write your answer in radical form (no calculator).
Which is the short side, which is the long side?
Short side = p = x
Long side = m = x√3
Hypotenuse = 18 = 2x 30
18cm m 60 p
2x = 18 hypotenuse = 18 cm
x=9 short side = 9 cm
x√3= 9√3 long side = 9√3 cm

18. Ex 2) Find the value of each variable
Ex 2) Find the value of each variable. Keep your answers in radical form. 60
x cm 30 z
Hypotenuse = 2x = 16cm
Long Side = x√3 = z
Short Side = x
Hypotenuse:
2x =16
Short Side
x = 8cm
Long Side: 8√3

19. CLASS WORK Page 550 #1-3 Page 552 #2-22 (even) Page 553 #24-34 (even)