funtrig presentation
- 1. Two Problems on the Application of Fundamentals of Trigonometry SUBMITTED TO: PROF. LAWAS SUBMITTED BY: GIANNE ITARALDE T/TH 9:40-11:10 CLASS
- 2. Problem #1 A boat with only one passenger is lost at sea. The passenger, being tired and all, is losing hope that he might not find land anymore and so, he slept. After a few hours, he woke up and saw a 115-feet high lighthouse from a distance. The angle of elevation from the boat to the top of the lighthouse is 10°. How far does he need to travel to get to land?
- 3. Illustration 1 1 5 f e e t 10 ° _?_ feet
- 4. Solution A Angle: Line: 115 feet A = 80 ° a = 652.1974 ft B = 10 ° b = 115 ft. c C = 90 ° b 10 ° C unknown B a To find Angle A: Line a: Tan A = _a_ 80= _a_ 115 (Tan –180 ==(90 + Angle Tan Tan A Angle 652.1974–_a_)°115 Side = = A =80°A = = C Angle= Opposite(AngleaAdjacent B) A a 115 (5.6713)feet 10) 180 Side / a 652.1974 80 Angle b 115 115 EquationAnswerfor Tan sum of Angles Equation(SOH-CAH-TOA) Substitute (Subtract the 80° Solve Multiply Answer Equation (SOH-CAH-TOA) C and Multiply both sides by 115 B from 180 °) Tan A is equal to a divided by b Substitute
- 5. Answer to Problem #1 The passenger needs to travel 652.1974 feet to get to land. 652.1974 feet
- 6. Problem #2 The leaning tower of Pisa is tilted at an angle of 4.6° from the vertical. An observer standing 100m from the base of the tower measures the angle of elevation to be 30°. Find the height of the tower.
- 7. Illustration _?_ m 100m 30°
- 8. Solution A Angle: Line: A = 64.6° a = 100m B = 30° b = 55.3526m 4.6° b c C = 85.4° 100m 30° C a B To find Angle C: Line b: A: 10064.6 Sin 50 b 0.9033=== =Sin )0.5 Sin0.9033 0.5= 30 ) 100 b ( ( 0.9033 __50__ Sin A (0.9033) = B b 100 A 85.4° (30 Angle C = 90 –-4.6 ° +85.4 °) = 55.3526m 64.6° 180 0.9033 b b b b 100 a 100 0.9033 b Solve andSin sum of 90your 30and Subtract 4.6 ° sidesbe the answer C from 180 Multiply both will and Sin Solve for both fromLaw°of B Substitutethatsides by b Sines) Equationthesides byby 100 answer Angles Divide both 64.6 Multiply (Use the 0.9033 Law of Sines: Sin A/a = Sin B/b = Sin C/c
- 9. Answer to Problem #2 The Leaning Tower of Pisa is 55.3526m high.
- 10. End of Presentation GIANNE ITARALDE’S PROJECT FOR FUNTRIG SOURCES OF IMAGES: •H T T P : / / S T A T I C . D D M C D N . C O M •H T T P : / / W W W . D R A G O A R T . C O M •H T T P : / / D A T A . G R E A T B U I L D I N G S . C O M •H T T P : / / B O U . M E