Trigonometry Chapter 1 Right Triangles v Mr Pines

Trigonometry Chapter 1 Right Triangles

v Mr. Pines classroom 802 is approximately 193 yards from the Main Office at Rancho. v Mr. Patterson’s classroom is only 72 yards from Mr. Pines classroom. v These 3 locations form a triangle. v Draw this triangle labeling all important information. Are you having trouble drawing this triangle? If you know where Mr. Patterson’s room it is possible.

v CASE 1 v Let’s consider that the angle formed at Mr. Patterson’s room is a right angle. Does this help? v How many different ways can you draw this triangle? v Can you find the measure of the other 2 angles? v If not the exact measures, can we estimate? What types of angles are these? v What should all the angles add up to? v How far is Mr. Patterson’s room from the main office? v What do we know for sure about this distance without making an calculations?

v CASE 2 v Let’s say that some of the distances in CASE 1 were incorrect. It appears that the angle formed at Mr. Patterson’s room is a right angle, and that the angle formed at the office is 30 degrees. The only correct distance is that room 802 is 72 yards from Mr. Patterson’s room. v What is the relationship between the sides? v Solve the remaining pieces of the triangle?

30 -60 -90 triangle Hypotenuse = 2(short leg) Long Leg = √ 3(short leg) c) If the short leg is 9 feet, what are the lengths of the long leg and hypotenuse? d) If the hypotenuse is 8 centimeters, what are the lengths of the two legs?

45 -45 -90 triangle Hypotenuse = √ 2(leg) a) If each leg is 8 ft, how long is the hypotenuse? b) If the hypotenuse is √ 10 feet, how long is each leg?

Special Right Triangles

Special Right Triangles

Special Right Triangles

Special Right Triangles

Special Right Triangles

Special Right Triangles

Angles are supplementary……which means they add to 180 degrees. What is the value of x?

The three angles ALWAYS add up to 180 degrees. a) If α=110° and β=45°, find γ b) If γ=βand α=3β, find all three angles.

Pythagorean Theorem a 2 + b 2 = c 2 c) If a = 6 and c = 10, find b d) If a = 6 and b = 5, find c e) If b = √ 7 and c = 10, find a

NFL CHALLENGE

NFL CHALLENGE As a group answer all questions on the NFL questionnaire You do not need to write the city name, just the mascot Example: Los Angeles Rams…. . . just write RAMS Use your cell phones Use Google, Find an NFL site, search for predictions, etc After the SUPER BOWL in Febuary, we will see who wins, . . . baseball cards awarded to best group. . . we will use this data in class later You have 15 minutes. . . GO

NFL CHALLENGE

Trigonometric Values v SOH CAH TOA Sin = Opp/Hyp Csc = Hyp/Opp Cos = Adj/Hyp Sec = Hyp/Adj Tan = Opp/Adj Cot = Adj/Opp Sin = y/r Csc = r/y Cos = x/r Sec = r/x Tan = y/x Cot = x/y

a) Find the value of x. b) Find the 6 trig function values.

Trigonometric Values Find the 6 trig function values at the points: a) (-4, 5) b) (2, 5) c) (-3, -10)

Solving Right Triangles

Solving Right Triangles

Solving Right Triangles

Solving Right Triangles 12

Solving Right Triangles A 12. 2 C 19. 3 B

Solving Right Triangles A 16 9 C B

Solving Right Triangles A 12. 4 C 18. 3 B

Solving Right Triangles A 12. 4 C 18. 3 B

Solving Right Triangles A 65° 41’ 5. 92 C B

Solving Right Triangles A 19 32° 23’ 29” C B

Google Maps 1. Using your cell phone find Rancho and 2 other locations in Garden Grove that form a right triangle. Sketch the triangle labeling all vertices, distances, and angle measures. Round side lengths to the nearest tenth of a mile. 2. Using your cell phone find Rancho and 2 other locations in Garden Grove that form a special right triangle. Either a 30 -60 -90, or a 45 -45 -90 triangle. Sketch the triangle labeling all vertices, distances, and angle measures. Round side lengths to the nearest tenth of a mile. v Hint: choose locations that are close to the street.

Degrees, Minutes, Secon ds 1 Degree° = 60 Minutes’ 1 Minute’ = 60 Seconds” Ex 1: Add the degrees and minutes 51° 29’ + 32° 46’ Ex 1: Add the degrees and minutes 90° - 73° 12’ 84° 15’ 16° 48’

Conversions Convert 34. 817° to degrees, minutes, and seconds.

Conversions Convert 74° 8’ 14” to decimal degrees.

Conversions Practice To Deg, Min, Sec a) 122. 6853° b) 89. 9004° To Decimal Degrees c) 274° 18’ 59” d) 165° 51’ 9”

Trigonometric Values Find the 6 trig function values at the point (3, -4)

Trigonometric Values v Find all 6 trig function values given the equation 3 x-y = 0, x>0 Start out by choosing a convenient value for x.

Trigonometric Values v Find all 6 trig function values given the following equations: a) 2 x-5 y = 0, x<0 b) 3 x+7 y =0, x>0