Elementary Trigonometry |
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Page 43
... min- utes the angular elevation of the top of the hill to an observer in the balloon is 30 ° : find the rate of the balloon's ascent in miles per hour . Example III . From the top of a cliff 150 VI . ] 43 EASY PROBLEMS .
... min- utes the angular elevation of the top of the hill to an observer in the balloon is 30 ° : find the rate of the balloon's ascent in miles per hour . Example III . From the top of a cliff 150 VI . ] 43 EASY PROBLEMS .
Page 46
... miles . NI S 4 miles 450 15 ° Example 2. At 9 A.M. a ship which is sailing in a direction E. 40 ° S. at the rate of 8 miles an hour observes a fort in a direction 50 ° North of East . At 11 A. M. the fort is observed to bear N. 20 ° W ...
... miles . NI S 4 miles 450 15 ° Example 2. At 9 A.M. a ship which is sailing in a direction E. 40 ° S. at the rate of 8 miles an hour observes a fort in a direction 50 ° North of East . At 11 A. M. the fort is observed to bear N. 20 ° W ...
Page 47
... miles 20 E Also S LACN ' L CAS 90 ° - 40 ° = 50 ° ; = : . LACB = LACN'- LBCN ' = 50 ° - 20 ° 30 ° . In the right - angled triangle ACB , AB AC tan ACB = 16 tan 30 ° : √ / 3 16 = = 16/3 3 = 9.237 nearly ; 2 √3 3 32√318-475 nearly ...
... miles 20 E Also S LACN ' L CAS 90 ° - 40 ° = 50 ° ; = : . LACB = LACN'- LBCN ' = 50 ° - 20 ° 30 ° . In the right - angled triangle ACB , AB AC tan ACB = 16 tan 30 ° : √ / 3 16 = = 16/3 3 = 9.237 nearly ; 2 √3 3 32√318-475 nearly ...
Page 48
... miles away from the lighthouse and continues to see it for 30/2 minutes . What is the speed of the steamer ? 5. A ship sailing due S. observes two lighthouses in a line exactly W. After sailing 10 miles they are respectively N.W. and ...
... miles away from the lighthouse and continues to see it for 30/2 minutes . What is the speed of the steamer ? 5. A ship sailing due S. observes two lighthouses in a line exactly W. After sailing 10 miles they are respectively N.W. and ...
Page 59
... mile ? T = 22 Let r yards be the radius of the circle ; then 2πr circumference = 792 ; = .. T = 792 792 × 7 = 2π 2 x 22 = 126 . Let a yards be the length of the arc traversed in each minute ; then from the formula a = r0 , 126 × 20 a ...
... mile ? T = 22 Let r yards be the radius of the circle ; then 2πr circumference = 792 ; = .. T = 792 792 × 7 = 2π 2 x 22 = 126 . Let a yards be the length of the arc traversed in each minute ; then from the formula a = r0 , 126 × 20 a ...
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Common terms and phrases
1+cos 1+tan² a+cos A+sin A+tan acute angle angle of elevation angles of depression B+cos B+sin bisecting centre circle cos² cos³ cosec cosine cot² cyclic quadrilateral decimal denote diff equal equation ex-central triangle Example expression Find the angle find the area find the distance find the height Find the number Find the value flagstaff following identities formula fraction given log greatest angle Hence horizontal plane hypotenuse inscribed integer LAOB loga magnitude mantissa miles negative number of radians observer pedal triangle perpendicular Prove the following quadrant radian measure radius vector regular polygon right angle right-angled triangle sec² sexagesimal shew Similarly sin sin sin sin² sin³ sine solution solve the triangle subtends an angle supplementary angles tan² tangent tower triangle ABC trigonometrical functions trigonometrical ratios
Popular passages
Page 131 - ... the logarithm of a fraction is equal to the logarithm of the numerator diminished by the logarithm of the denominator...
Page 179 - From a station, B, at the base of a mountain, its summit A is seen at an elevation of 60° ; after walking one mile towards the summit, up a plane making an angle of 30° with the horizon, to another station, C, the angle BCA is observed to be 135° : find the height of the mountain in yards.
Page 350 - OF EUCLID'S ELEMENTS. Including Alternative Proofs, together with additional Theorems and Exercises, classified and arranged. By HS HALL, MA, and FH STEVENS, MA, Masters of the Military and Engineering Side, Clifton College. Gl.
Page 132 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Page 39 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius of the circle...
Page 132 - Let N be a number whose integral part contains n digits ; then JV= JQ<il>HftiMlon . .'. log^V=(?t— l) + a fraction. Hence the characteristic is и — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and is positive.
Page 187 - From the top of a hill the angles of depression of two objects situated in the...
Page viii - ... equal parts, called degrees; a degree into 60 equal parts, called minutes; a minute into 60 equal parts, called seconds. Degrees, minutes, and seconds are indicated in connection with numbers by the respective symbols °, ', ". 25 degrees, 18 minutes, 34 seconds is written 25° 18
Page xi - Ratio is the relation which one quantity bears to another of the same kind, with reference to the number of times that the one is contained in the other.
Page 348 - We will not say that this is the best Elementary Algebra for school use that we have come across, but we can say that we do not remember to have seen a better. . . . It is the outcome of a long experience of schoolteaching, and so is a thoroughly practical book. All others that we have in our eye are the works of men who have had considerable experience with senior and junior students at the universities, but have had little...