Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página x
... heights and distances 49 • 3539 50 30. Problems requiring a knowledge of the points of the mariner's compass 53 31. Mensuration 32. Solution of isosceles triangles 33. Related regular polygons and circles 34. Solution of oblique ...
... heights and distances 49 • 3539 50 30. Problems requiring a knowledge of the points of the mariner's compass 53 31. Mensuration 32. Solution of isosceles triangles 33. Related regular polygons and circles 34. Solution of oblique ...
Página xii
... heights and distances 64. Summary CHAPTER VIII . SIDE AND AREA OF A TRIANGLE . CIRCLES CONNECTED WITH A TRIANGLE . 65. Length of a side of a triangle in terms of the adjacent sides and the adjacent angles 66. Area of a triangle 67. Area ...
... heights and distances 64. Summary CHAPTER VIII . SIDE AND AREA OF A TRIANGLE . CIRCLES CONNECTED WITH A TRIANGLE . 65. Length of a side of a triangle in terms of the adjacent sides and the adjacent angles 66. Area of a triangle 67. Area ...
Página 9
... heights , and distances . An acquaintance with its simpler results is very helpful , and sometimes indispensable , in even a brief study of such sciences as astronomy , physics , and the various branches of engineering . Some modern ...
... heights , and distances . An acquaintance with its simpler results is very helpful , and sometimes indispensable , in even a brief study of such sciences as astronomy , physics , and the various branches of engineering . Some modern ...
Página 14
... height of an equilateral triangle whose side is 20 yd . 8. The side of an isosceles triangle is 40 ft . and the base is 30 ft .; find the height . 9. What is the length of the diagonal of a square whose side is 20 ft . ? 10. What is the ...
... height of an equilateral triangle whose side is 20 yd . 8. The side of an isosceles triangle is 40 ft . and the base is 30 ft .; find the height . 9. What is the length of the diagonal of a square whose side is 20 ft . ? 10. What is the ...
Página 50
... heights and distances . instruments used for measuring angles . The sextant can be used for measuring the angle between the two lines drawn from the observer's eye to each of two distant objects . Horizontal and vertical angles can be ...
... heights and distances . instruments used for measuring angles . The sextant can be used for measuring the angle between the two lines drawn from the observer's eye to each of two distant objects . Horizontal and vertical angles can be ...
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Términos y frases comunes
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Pasajes populares
Página 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Página 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.
Página 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Página vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Página 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Página 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Página 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Página 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.