Plane Trigonometry |
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Page 40
... horizontal line N drawn through O to meet in M the vertical line drawn through P. The angle MOP is called the Angle ... horizontal . This table being at O and horizontal and the telescope Simple problems in Heights and Distances.
... horizontal line N drawn through O to meet in M the vertical line drawn through P. The angle MOP is called the Angle ... horizontal . This table being at O and horizontal and the telescope Simple problems in Heights and Distances.
Page 41
... horizontal , i.e. gives us the angle of elevation MOP . Similarly , if the instrument were at P , the angle NPO through which the telescope would have to be turned , downward from the horizontal , would give us the angle NPO . The ...
... horizontal , i.e. gives us the angle of elevation MOP . Similarly , if the instrument were at P , the angle NPO through which the telescope would have to be turned , downward from the horizontal , would give us the angle NPO . The ...
Page 42
... horizontally , so that EAC - 30 ° and LEAD = 60 ° . Let r feet be the height of the tower and produce DC to meet AE in E , so that CE = AB - x = 200 – x . Since △ ADB = 4 DAE = 60 ° ( Euc . 1. 29 ) , .. DB = AB cot ADB = 200 cot 60 ...
... horizontally , so that EAC - 30 ° and LEAD = 60 ° . Let r feet be the height of the tower and produce DC to meet AE in E , so that CE = AB - x = 200 – x . Since △ ADB = 4 DAE = 60 ° ( Euc . 1. 29 ) , .. DB = AB cot ADB = 200 cot 60 ...
Page 43
... horizontal plane and finds that the angle of elevation is then 30 ° ; find the height of the tower and his original distance from it . B 44 A / 60 % B A M P 300 √3.x 30 ° B X√3 Xx ४ M Ax M √3 Let P be the top , and PM the height ...
... horizontal plane and finds that the angle of elevation is then 30 ° ; find the height of the tower and his original distance from it . B 44 A / 60 % B A M P 300 √3.x 30 ° B X√3 Xx ४ M Ax M √3 Let P be the top , and PM the height ...
Page 44
... horizontal line through its base , the angular elevation of its top changes from 30 ° to 45 ° . 5. An observer on the top of a cliff , 200 feet above the sea - level , observes the angles of depression of two ships at anchor to be 45 ...
... horizontal line through its base , the angular elevation of its top changes from 30 ° to 45 ° . 5. An observer on the top of a cliff , 200 feet above the sea - level , observes the angles of depression of two ships at anchor to be 45 ...
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Common terms and phrases
a+b+c a+ẞi A₁ ad inf angle AOP angle of elevation Binomial Theorem centre circle circumcircle coefficient complex quantity cos¹ cos² cos³ cosec cosh cosine cotangent denoted Diff distance equal EXAMPLES expression feet Find the angle find the height find the values flagstaff given log Hence infinite inscribed integer last article length loga logarithm loge miles multiple nearly number of radians pedal triangle perpendicular places of decimals principal value prove quadrant quadrilateral r₁ radius regular polygon revolving line right angle sec² secant shew shewn sides Similarly sin sin sin sin¹ sin² sin³ sine sinh tan-¹ tan² tan³ tangent tanh Theorem tower triangle ABC trigonometrical functions trigonometrical ratios unity x+yi zero α α π π
Popular passages
Page 36 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 17 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 44 - A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 50°; walking 40 ft.
Page 13 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef.
Page 1 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 10 - If the radius of the earth be 4000 miles, what is the length of its circumference?
Page 42 - From the top of a cliff 150 ft. high the angles of depression of the top and bottom of a tower are 30° and 60°, respectively.
Page 220 - A ladder placed at an angle of 75° just reaches the sill of a window at a height of 27 feet above the ground on one side of a street. On turning the ladder over without moving its foot, it is found that when it rests against a wall on the other side of the street it is at an angle of 15° with the ground.
Page 215 - From the top of a hill the angles of depression of two objects situated in the...