Have out:

1. 50 ft 120 ft ??? +1 +1 +1 +2 +1 170 tan8= x 170 ft 170 x= tan8 8 x U7D7 Have out: Pencil, highlighter, red pen, GP NB, textbook, homework Bellwork: If a jet climbs at an angle of 8, what is the minimum distance between its take-off point & a 120 foot tower, so the jet will clear the tower by at least 50 feet? x  1209.61 ft The plane needs to start at least 1209.61 ft away.

2. You have 10 minutes to complete the resource page with the person next to you!

3. Length of legs Length of hypotenuse Fig. # 5 4 1 units 2 4 units units units units units 5 3 In a 45-45-90 , the hypotenuse is always times longer than the legs. 4 5 n a) Look for a pattern in the first three figures. Draw figures 4 & 5, and solve for the length of the hypotenuse in the last figure drawn. Fill in the table and then state your observations. T-61 What kind of triangles are shown in the pictures below? We will refer to these as 45-45-90s. Isosceles Right Triangles 3 2 1 3 1 2 1 unit 2 units 3 units 4 units 5 units n units

4. T-62 Here is another way to understand the isosceles right triangle relationship… 45 90 a) Draw in one diagonal & shade in one of the right triangles formed. x b) Label the angle measures in the other right triangle. 45 x c) If one leg has a length of x, what is the length of the other leg? Why? The other leg also has a length of x, since the sides of a square are always equal by definition. d) What is the length of the hypotenuse in terms of x? (Use the Pythagorean Theorem & write in simple radical form.) (Pythagorean Thm.)

5. 30 30 c = ? 30 b = ? 6 30 4 2 60 60 60 60 n 1 2 3 Fig. # Short leg Long leg hypotenuse units 1 units units units units units In a 30-60-90 ,the hypotenuse is twice the length of the short leg. The long leg is times the short leg. 2 3 4 30 5 30 n 8 10 60 60 5 4 T-63 Below are what we refer to as 30-60-90 s. “short leg”: leg opposite the 30. “long leg”: leg opposite the 60. 1 unit 2 units 2 units 4 units 6 units 3 units 8 units 4 units 5 units 10 units n units 2n units

6. T-64 Here is another way to understand the 30-60-90 triangle relationship… a) Draw in a height & shade in one of the right triangles formed. 30 2x b) Label the angle measures in the other right triangle. 90 60 x c) If the hypotenuse has a length of 2x, what is the length of the short leg? Why? The short leg has a length of x, since the height of an equilateral triangle bisects the base. (We proved this in T-52!!) d) What is the length of the long leg in terms of x? (Use the Pythagorean Theorem & write in simple radical form.) (Pythagorean Thm.)

7. Why do we need to know these????? Side ratio of 1:1: Legs: n Hypotenuse: n 45 n 45 n 30 Side ratio of 1: :2 2n Short Leg: n Long Leg: n Hypotenuse: 2n 60 n Special Triangle Formulas Add to your notes... 45- 45- 90 Triangle: OR • They give EXACT answers. • They are quicker & more convenient than trig. • You need them on the SAT test! 30- 60- 90 Triangle: OR

8. x 45 8 30 y 8 Legs: n y 45 Hypotenuse: n 60 x Short Leg: n Long Leg: n Hypotenuse: 2n Find the values for x and y in each triangle without using your calculator. (Give exact answers!) T-65 a) b) 30- 60- 90 Triangle: 45- 45- 90 Triangle: = 4u = 8u = 4 u = 8 u = 8u 2n = 8 x = 4u x = 8u 2 2 y = 4 u n = 4 y = 8 u

9. Legs: n Hypotenuse: n Find the perimeter of a square which has a diagonal of length 5 . Show how you obtained your answer. T-66 45- 45- 90 Triangle: = 5u n = 5 P = 4n = 4(5) = 20 u

10. Finish T 67-74