Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página xi
... sides and angles of a triangle . The law of sines . The law of cosines . 98 54a . Substitution of sines for sides , and of sides for sines 101 55. Case I. Given one side and two angles . 101 56. Case II . 57. Case III . Given two sides ...
... sides and angles of a triangle . The law of sines . The law of cosines . 98 54a . Substitution of sines for sides , and of sides for sines 101 55. Case I. Given one side and two angles . 101 56. Case II . 57. Case III . Given two sides ...
Página xii
... 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 of a quadrilateral in terms of its diagonals ...
... 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 of a quadrilateral in terms of its diagonals ...
Página 12
... side of a square is one foot in length , then the length of a diagonal of the square is √2 feet . Thus the ratio of the diagonal to the side is √2 , a number which cannot be expressed as the ratio of two whole numbers . Two quantities ...
... side of a square is one foot in length , then the length of a diagonal of the square is √2 feet . Thus the ratio of the diagonal to the side is √2 , a number which cannot be expressed as the ratio of two whole numbers . Two quantities ...
Página 14
... 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 length of the side of a square 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 length of the side of a square whose ...
Página 20
... side ; ( b ) the two sides about the right angle ; ( c ) the hypotenuse and one of the acute angles ; ( d ) one of the sides about the right angle and the opposite angle ; ( e ) one of the sides about the right angle and the adja- cent ...
... side ; ( b ) the two sides about the right angle ; ( c ) the hypotenuse and one of the acute angles ; ( d ) one of the sides about the right angle and the opposite angle ; ( e ) one of the sides about the right angle and the adja- cent ...
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Términos y frases comunes
A+B+C acute angles algebraic centre CHAPTER circumscribing computation construction cos² cosec cosine cotangent deduced definitions denoted derived diedral angle draw equal equation EXAMPLES expression figure formulas geometry height Hence hypotenuse included angle inscribed circle intersection isosceles triangle law of cosines law of sines length logarithms M₁ method negative NOTE number of degrees number of sides OP₁ opposite perpendicular Plane Trigonometry polar triangle pole positive angles quadrant QUESTIONS AND EXERCISES radian measure radius regular polygon relations respectively revolving right angles right-angled triangle sec² secant Show shown sides and angles sin² sine solid angle Solve ABC sphere spherical angle spherical degrees spherical excess spherical polygon spherical triangle spherical trigonometry subtended tan² tangent terminal line tower triangle ABC triedral trigono trigonometric functions trigonometric ratios whole number
Pasajes populares
Página 35 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Página 25 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 87 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 85 - 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 and the cosine of their included angle.
Página 55 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Página 111 - The ratio of a circumference of a circle to its diameter is the same for all circles. [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance, to Euclid VI., 33.* The proof of (6) is not contained in all geometries ; for instance, Euclid does not give...
Página 183 - 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 41 - Geometry that 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 THE RIGHT TRIANGLE.