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 hypotenuseSide opposite 45° angle is ½ the hypotenuse times √2Side opposite 60° angle is ½ the hypotenuse times √3

a

b

alt = √ab

alt

45

45

6

3√2

6 3

3√3

30

60

5-Minute Check on Lesson 7-35-Minute Check on Lesson 7-35-Minute Check on Lesson 7-35-Minute Check on Lesson 7-3 Transparency 7-4

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Find x and y.

1. 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.?Standardized Test Practice:

A CB D5 5√3 (5/3)√3 10

xy°10

x = 16

y = 16√3

P = 60 cm

(-3,3)

B

x = 5√2

y = 45°30°y

x

10.5√3 ≈ 18.19 in

32

C D

E

3x°

6x°

Lesson 7-4a

Right Triangle Trigonometry

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

Trig Definitions

• Sin (angle) =

• Cos (angle) =

• Tan (angle) =

Opposite----------------Hypotenuse

Adjacent----------------Hypotenuse

Opposite ---------------- Adjacent

S-O-H

C-A-H

T-O-A

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

θ hypotenuse

A

BC

Example:

opposite side BCsin A = sin θ = ---------------------- = ------ hypotenuse AB

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 BCsin θ = sin 30 = 0.5 = ---------------------- = ----- = ------ hypotenuse AB 14

(14) 0.5 = BC = 7

Anatomy of a Trig Function

θ hypotenuse

A

BCUse 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

Example:

opposite side BCsin A = sin θ = ---------------------- = ------ hypotenuse AB

If BC = 7 and AB = 14, then to find A or θ we have

opposite side BC 7sin θ = ---------------------- = ----- = ----- = 0.5 A = θ = sin-1(0.5) = 30° hypotenuse AB 14

Anatomy of a Trig Function

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

Answer:

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:

Example 3

Use a calculator to find tan to the nearest ten thousandth.

KEYSTROKES: 56 1.482560969TAN ENTER

Answer:

KEYSTROKES: 90 0COS ENTER

Answer:

Use a calculator to find cos to the nearest ten thousandth.

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.

Example 4

Answer:

Answer:

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