Elementary Trigonometry: With a Collection of ExamplesDeighton, Bell, and Company, 1862 - 184 páginas |
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Página 107
... feet , to find d approximately , and the amount of error in the value obtained of d if h2 be neglected . R2 Taking R to be 4000 miles , by substitution in the formula we shall get d2 = 2Rh , d = 551478'09 inches , which is between 8 and ...
... feet , to find d approximately , and the amount of error in the value obtained of d if h2 be neglected . R2 Taking R to be 4000 miles , by substitution in the formula we shall get d2 = 2Rh , d = 551478'09 inches , which is between 8 and ...
Página 109
... feet ? The numerical measure of any magnitude is the ratio which it bears to the magnitude which is taken as the unit of measure- m ment . Now the ratio of m feet or yards to n yards is 3 which is therefore the numerical measure of m ...
... feet ? The numerical measure of any magnitude is the ratio which it bears to the magnitude which is taken as the unit of measure- m ment . Now the ratio of m feet or yards to n yards is 3 which is therefore the numerical measure of m ...
Página 113
... feet by an arc whose length is 7 inches . Ans . 6 ° 40 ′ 54 ′′ 52 . 26. Shew that the length of an arc subtending an angle of 14 ° 29 ′ 24 ′′ in a circle , the radius of which is 1000 yards , is 252 yds . 2 ft . 8 in . nearly . 27 ...
... feet by an arc whose length is 7 inches . Ans . 6 ° 40 ′ 54 ′′ 52 . 26. Shew that the length of an arc subtending an angle of 14 ° 29 ′ 24 ′′ in a circle , the radius of which is 1000 yards , is 252 yds . 2 ft . 8 in . nearly . 27 ...
Página 175
... feet of the perpendiculars from the angle of a triangle ABC upon the sides , prove that the radius of the circle circumscribing the triangle A'B'C ' is half that of the circle circumscribing ABC . 37. A circle is described about a ...
... feet of the perpendiculars from the angle of a triangle ABC upon the sides , prove that the radius of the circle circumscribing the triangle A'B'C ' is half that of the circle circumscribing ABC . 37. A circle is described about a ...
Página 178
... feet apart . A person standing at the foot of each tower observes the angle of elevation of one tower to be double that of the other , but when he is halfway between them , the angle of elevation of one tower is the complement of the ...
... feet apart . A person standing at the foot of each tower observes the angle of elevation of one tower to be double that of the other , but when he is halfway between them , the angle of elevation of one tower is the complement of the ...
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Términos y frases comunes
a+b+c a²+b² angle AOP angle of elevation angular arithmetical progression B-sin bisecting centre circular measure circumference circumscribing circle cos² cos³ cosec cosine decimal decreases in magnitude determined distance equal escribed circles EXAMPLES ILLUSTRATING CHAPTER feet Find the number find the value formula Given log given value Hence horizontal plane increases inscribed integer logarithm mount Ebal number of degrees number of grades Observe the angles perpendicular polygon Prove Quadrant quadrilateral radii radius regular polygon respectively revolving line right angle sec² secant secondary angle shew sides sign and magnitude similar triangles Similarly sin A sin sin A+B sin² sin³ sine sines and cosines Solve the equation solve the triangle straight line subtend tan² tangent tower triangle ABC trigono trigonometrical functions versin π π пп
Pasajes populares
Página 64 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 1 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 175 - ... 66. Construct an equilateral triangle, having given the length of the perpendicular drawn from one of the angles on the opposite side. 67. Having given the straight lines which bisect the angles at the base of an equilateral triangle, determine a side of the triangle. 68. Having given two sides and an angle of a triangle, construct the triangle, distinguishing the different cases. 69. Having given the base of a triangle, the difference...
Página 37 - B + cos A . sin B tan(A + B)= ) , (- = — . --. v cos (A + B) cos A . cos B — sin A . sin B and dividing numerator and denominator by cos A . cos B, sin A sin B cos A "'"cos B tan A + tan B 1 tan A.
Página 175 - Three circles are described, each of which touches one side of a triangle ABC, and the other two sides produced. If D be the point of contact of the side BC, E that of AC, and F that of AB, shew that AE is equal to BD, BF to CE, and CD to AF.
Página 5 - Now the angle at the centre of a circle which is subtended by an arc equal to the radius equals — = 57°. 29578, it so that the true length of a curve is given by the equation t IR L — ~ — — 57.2958 — 57.2958...
Página 113 - ... would be subtended at the centre of the first by an arc equal to the radius of the second. 9. If a be the arc which measures the complement of an angle to radius r, find the arc which measures the supplement of the same angle to radius r'.
Página 159 - It is required to bisect any triangle (1) bya line drawn parallel, (2) by a line drawn perpendicular, to the base. 43. To divide a given triangle into two parts, having a given ratio to one another, by a straight line drawn parallel to one of its...