Elementary Trigonometry |
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Page 5
... yards to 2 × 3 × 12 8 27 inches is measured by the fraction 27 or དྷ་ OBS . Since a ratio expresses the number of times that one quantity contains another , every ratio is a numerical quantity . 10. DEFINITION . If the ratio of any two ...
... yards to 2 × 3 × 12 8 27 inches is measured by the fraction 27 or དྷ་ OBS . Since a ratio expresses the number of times that one quantity contains another , every ratio is a numerical quantity . 10. DEFINITION . If the ratio of any two ...
Page 42
... yards high , given that the angle of elevation is 41 ° 18 ' , and that sin 41 ° 18 ' = ' 66 . 8. One chimney is 30 yards higher than another . A person standing at a distance of 100 yards from the lower observes their tops to be in a ...
... yards high , given that the angle of elevation is 41 ° 18 ' , and that sin 41 ° 18 ' = ' 66 . 8. One chimney is 30 yards higher than another . A person standing at a distance of 100 yards from the lower observes their tops to be in a ...
Page 43
... yards nearer the elevation is found to be 60 ° : find the height of the tower . 10. A flagstaff stands upon the top of a building ; at a distance of 40 feet the angles of elevation of the tops of the flagstaff and building are 60 ° and ...
... yards nearer the elevation is found to be 60 ° : find the height of the tower . 10. A flagstaff stands upon the top of a building ; at a distance of 40 feet the angles of elevation of the tops of the flagstaff and building are 60 ° and ...
Page 44
... yards . 18. From the top of a lighthouse 80 yards above the horizon the angles of depression of two rocks due west of the observer are 75 ° and 15 ° : find their distance apart , given cot 75 ° = · 268 and cot 15 ° = 3.732 . 50 ...
... yards . 18. From the top of a lighthouse 80 yards above the horizon the angles of depression of two rocks due west of the observer are 75 ° and 15 ° : find their distance apart , given cot 75 ° = · 268 and cot 15 ° = 3.732 . 50 ...
Page 47
... yards one of the objects is due N. of him , and the other lies N.W .: how far was he from the objects at first ? 2. Sailing due E. I observe two ships lying at anchor due S .; after sailing 3 miles the ships bear 60 ° and 30 ° S. of W ...
... yards one of the objects is due N. of him , and the other lies N.W .: how far was he from the objects at first ? 2. Sailing due E. I observe two ships lying at anchor due S .; after sailing 3 miles the ships bear 60 ° and 30 ° S. of W ...
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Common terms and phrases
1+cos 1+tan² a+cos a+sin a+ß A+tan acute angle angle of elevation B+cos centre circle cos A cos cos² cos³ cosec cosine cot² cyclic quadrilateral decimal denote diff equal equation ex-central triangle Example expression feet Find the angle 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 integer loga magnitude mantissa miles negative number of radians obtain pedal triangle perpendicular positive Prove the following quadrant quadrilateral quantities radian measure radius vector regular polygon right angle right-angled triangle sec² sexagesimal shew sin A sin sin sin sin sin² sin³ sine solution solve the triangle supplementary angles tan² tangent tower triangle ABC trigonometrical functions trigonometrical ratios whence Зп
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...