Welcome to your Trigonometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. P and Q are two places on the equator. The shortest distance between them along the equator is 8500 km. Find the angle between P and Q. (Take R =6,370 km, π= 3.142) 76.4° 24° 14° 121° 2. Three cities London, Seoul and Harare are such that Seoul is located 50 km away from London on a bearing of 065°. Harare is 100 km away from London on a bearing of 305°. The distance between Seoul and Harare is 50√2 km 50√3 km 50√7 km 50√5 km 3. Three locations on the surface of the earth are Mumbai(45°N, 20ºE), Guanzhou(45°N, 40°E) and Ibadan(45°S, 40°E). Which of the following statements are correct?I. Guanzhou and Ibadan are on the same longitude.II. Guanzhou and Ibadan are on the same latitude.III. The difference between the longitudes of Mumbai and Guanzhou is 60°.IV. The difference between the latitudes of Mumbai and Ibadan is 90°. I and IV only II and III only I and III only II and IV only 4. A bearing of 310°, expressed as a compass bearing is N 40° W N 50°W S 50° W S 40° W 5. The value of is 1 0 -2 2 6. A right-angled triangle has sides of lengths (3m-1) cm, (m) cm and (3m+1) cm. The value of m is 18 2 12 6 7. The value of1 + sec²60° is 4 5 2 2 1/3 8. Starting from town X(45°N, 17°E), an airplane flies to town Y(45°N, 47°E) along the parallel of latitude and later to a third town Z(60°N, 47°E) along the meridian.(R = 6,370 km, π= 22/7). The distance between Y and Z along the meridian is 5,005 km 3,336 2/3 km 1,668 1/3 km 2,502 1/2 km 9. Point P(60°S,22°E) lies on the same latitude as point Q. If the distance PQ measured along the parallel of latitude is 5,oo5 km, the radius of the earth is 6.370 km and π = 22/7, the longitude of point Q is 68°W 67°E 30°E 30°W 10. If sin θ = a/b, where θ is an acute angle,then cot θ equals a/ √(b²-a²) √(b+a)(b-a)/ a √(b²-a²)/ b √(b/ b²-a²) 11. From the top of a 100m high building, a man observes the top of a tree at an angle of depression of 30°. If the tree is 50 m tall, the angle of depression of the foot of the tree as viewed by the man is tan-1(2√3/2) tan-1(√3) tan-1(2√3) tan-1(√3/2) 12. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to 3/4 5/4 5/3 4/3 13. If there is no stop-over at Dubai, and the average speed of the airplane is 500km/hr, the total time taken for the plane to fly from Lagos to Kuala Lumpur via Dubai is approximately 5 h 7 h 8 h 10 h 14. If cos θ = -½, the values of θ could be 120 or 300 degrees -60 or 240 degrees -60 or 120 degrees 120 or 240 degrees 15. A woman 1.65 m tall stood 50 m away from the foot of a tower and observed that the angle of elevation pf the top of the tower to be 50°. What is the height of the tower? 23m 61.2 m 12 m 24.5 m 16. Given that tan²θ + sec²θ = 3, the value of θ (for 0°<θ<90°) is 45 degrees 30 degrees 60 degrees 90 degrees 17. If cos θ = √3/2, evaluate (3-2√3)/ 3 1/2 (√3-2)/ 3 √3/2 -1 18. If cos θ = sin 50°, then θ is 90 degrees 45 degrees 50 degrees 40 degrees 19. The angle between latitudes 20°N and 74°N is 54° 62° 94° 74° 20. The values of θ for whichsin θ = cos θ are within the range 0° < θ < 360° 45° and 135° 135° and 225° 45° and 225° 45° and 315° 21. The bearing of a point P from an observer Q is S37°W. The bearing of Q from P is N 37° E S 53° W S 37° E N 53° W 22. The values of tan 225° and tan 315° are respectively -1 and 1 1 and -1 -1 and -1 1 and 1 23. X and Y are two lakes on the earth's surface. X has a latitude 34°N and Y has latitude 15°S. If the lakes are on the same meridian ,calculate the distance between them along the meridian(Take 2πR = 40,000 km) 540km 5440km 54km 23km 24. In a triangle PQR, <PQR = 60°, PQ = 3 cm and QR = 4 cm. Find |PR| 2√5 cm 2√3 cm 5 cm √13 cm 25. The two perpendicular sides of a right-angled triangle are 9 cm and 12 cm in length. The smallest angle of the triangle is 30 degrees 36 degrees 36.9 degrees 53.1 degrees 1 out of 25 Time is Up! Time's up