28/03/2020Trigonometry(Senior Class Maths Study by Topics) 0Comments by Gate Academy Welcome to your Trigonometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. From a point P 30 m away from the foot of a tree, the angle of elevation of the top of the tree is 30°. From a point Q on the opposite side of the tree, the angle of elevation of the top of the three is 45°. The distance between P and Q is42 m17.3 m47.3 m50 m2. If the bearing of New York from Kansas city is 125°, the bearing of Kansas city from New York is?235°215°305°55°3. The sine, cosine and tangent of 240° are, respectively√3/2, -1/2 and √3-√3/2, 1/2 and -√3√3/2, 1/2 and √3-√3/2, -1/2 and √34. Each of two angles of an isosceles triangle is 30° and the longest side of the triangle is 9 cm. Each of the other sides is of length3√2 cm9√2/2 cm3√3 cm9/2 cm5. A bearing of 310°, expressed as a compass bearing isS 50° WN 40° WN 50°WS 40° W6. Two cities are both on longitude 55°E. If their latitudes are 5°S and 65°S and R = 6,400 km, their distance apart in km is6,400π / 36,400π22,400π / 93,200π / 37. The pilot of an airplane flying at an altitude of 2 km observes a landmark at an angle of depression of 25°. A few seconds later, he observes the landmark at an angle of depression of 50°. The distance between the two points of observation in km is2(sin 50° - sin 25°)2(cos 25° - cos 50°)2(cot 25° - cot 50°)2(tan 50° - tan 25°)8. For any value of θ, the value ofiscos²θsin²θ129. An observer on the ground views an airplane of altitude 1,000 m at an angle of elevation of 30°. How far is the plane from the observer?1,000 m500 m2,000 m1154.7 m10. A motorist travels from Abuja on a bearing of 150° to Kaduna 40 km away. From Kaduna he travels to Lagos on a bearing of 210°.If Lagos is located directly South of Abuja, how far is Lagos from Abuja?40 km80 km40√2 km40√3 km11. The values of tan 225° and tan 315° are respectively1 and 1-1 and 11 and -1-1 and -112. If cos θ = √3/2, evaluate (√3-2)/ 3(3-2√3)/ 31/2√3/2 -113. The diagonals of a rhombus are of lengths 10 cm and 24 cm.The length of each side of the rhombus is13 cm17 cm12 cm5 cm14. Given that cos²θ - sin²θ = 1/8, find the value of tan θ3√73/√7√7√7/315. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to5/45/34/33/416. The bearing of N75°W can also be expressed as285°225°075°165°17. The value of 2cos 270° + sin 270° is0-21-118. 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 is1,668 1/3 km3,336 2/3 km2,502 1/2 km5,005 km19. Given that sin θ = 4/5, the value of (1 - cos²θ) for 0°< θ < 90° is9/259/162/516/2520. A ladder resting against a vertical wall makes an angle tan-¹(2.4) with the ground. If the foot of the ladder is 1 m from the wall, what is the length of the ladder?1 m2.6 m2.4 m5.2 m21. The angle between latitudes 47°S and 21°N is26°68°34°78°22. If sin-¹(0.966) = 75°, then sin-¹(-0.966) equals105 or 255 degrees75 or 105 degrees195 or 285 degrees255 or 285 degrees23. A girl walks 30 m from a point P on a bearing of 040º to a point Q. She then walks 30 m on a bearing of 140º to a point R. How far is R from P25.2 km30 km42.4 km38.6 km24. Simplify the expression can be simplified tocosθ1-sinθ(1+cosθ)/ sinθsinθ/(1-cosθ)25. The two perpendicular sides of a right-angled triangle are 9 cm and 12 cm in length. The smallest angle of the triangle is36 degrees53.1 degrees36.9 degrees30 degrees26 out of 25Time is Up!