Quiz 1 Need-to-Know

1. a b alt = √ab Quiz 1 Need-to-Know Arithmetic Mean (AM) or average: (a + b) / 2 Geometric Mean (GM): √ab Altitude = GM of divided hypotenuse Pythagorean Theorem: a2 + b2 = c2 Pythagorean Triples: Whole numbers that solve the theorem Side opposite 30° angle is ½ the hypotenuse Side opposite 45° angle is ½ the hypotenuse times √2 Side opposite 60° angle is ½ the hypotenuse times √3 alt 45 6 60 6 3 45 30 3√2 3√3

2. Transparency 7-4 5-Minute Check on Lesson 7-3 • Find x and y. • 2. • 3. The length of a diagonal of a square is 15√2 cm. Find the perimeter of the square. • 4. The side of an equilateral triangle measures 21 inches. Find the length of the altitude of the triangle. • 5. ∆MNP is a 45°- 45°- 90° triangle with right angle P. Find the coordinates of M in quadrant II with P(2,3) and N(2,8). • 6. In the right trianglefind CD if DE = 5.? x = 16 y = 16√3 x = 5√2 y = 45° 32 x y° 10 x 30° y P = 60 cm 10.5√3 ≈ 18.19 in (-3,3) C D Standardized Test Practice: 3x° 6x° 10 5 5√3 (5/3)√3 E B A B C D Click the mouse button or press the Space Bar to display the answers.

3. Lesson 7-4a Right Triangle Trigonometry

4. Trigonometric Functions • Main Trig Functions: • Sine sin -1 ≤ range ≤ 1 • Cosine cos -1 ≤ range ≤ 1 • Tangent tan -∞ ≤ range ≤∞ • Others: • Cosecant csc 1 / sin • Secant sec 1 / cos • Cotangent cot 1/ tan • Tangent sin / cos

5. Trig Definitions Opposite ---------------- Hypotenuse S-O-H • Sin (angle) = • Cos (angle) = • Tan (angle) = Adjacent ---------------- Hypotenuse C-A-H Opposite ---------------- Adjacent T-O-A

6. Ways to Remember • S-O-H • C-A-H • T-O-A Some Old Hillbilly Caught Another Hillbilly Throwing Old Apples Some Old Hippie Caught Another Hippie Tripping On Acid Extra-credit: Your saying

7. Anatomy of a Trig Function A Example: opposite side BC sin A = sin θ = ---------------------- = ------ hypotenuse AB θ hypotenuse C B Use trig functions to help find a missing side in a right triangle. Format: some side Trig Function ( an angle, θ for example) = ----------------------- some other side where the some side or the some other side is the missing side If θ = 30 and AB = 14, then to find BC we have opposite side BC BC sin θ = sin 30 = 0.5 = ---------------------- = ----- = ------ hypotenuse AB 14 (14) 0.5 = BC = 7

8. Anatomy of a Trig Function A Example: opposite side BC sin A = sin θ = ---------------------- = ------ hypotenuse AB θ hypotenuse C B Use inverse trig functions to help find a missing angle in a right ∆. Format: some side Trig Function -1 (-------------------------) = missing angle, θ for example some other side where the trig function -1 is found using 2nd key then the trig function on calculator If BC = 7 and AB = 14, then to find A or θ we have opposite side BC 7 sin θ = ---------------------- = ----- = ----- = 0.5 A = θ = sin-1(0.5) = 30° hypotenuse AB 14

9. Example 1 Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal. Answer:

10. Example 2 Find sin A, cos A, tan A, sin B, cos B, and tan B. Express each ratio as a fraction and as a decimal. Answer:

11. Use a calculator to find tan to the nearest ten thousandth. Use a calculator to find cos to the nearest ten thousandth. TAN ENTER KEYSTROKES: 56 1.482560969 COS ENTER KEYSTROKES: 90 0 Answer: Answer: Example 3

12. Answer: Answer: Example 4 a. Use a calculator to find sin 48° to the nearest ten thousandth. b. Use a calculator to find cos 85° to the nearest ten thousandth.

13. Summary & Homework • Summary: • Trigonometric ratios can be used to find measures in right triangles • Sin of an angle is opposite / hypotenuse • Cos of an angle is adjacent / hypotenuse • Tan of an angle is adjacent / hypotenuse • Homework: • pg 367-368; 1, 4, 5-8, 11, 15, 16