Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página 30
... ABC be an equilateral triangle . From any vertex B draw a perpendicular BD to the opposite side AC . Then angle DAB = 60 ° , an- gle ABD = 30 ° . √4a2 — a2 = a√3 . FIG . 12 . If AB = 2 a , then AD = a , and DB : = DB AB = ... sin 60 ...
... ABC be an equilateral triangle . From any vertex B draw a perpendicular BD to the opposite side AC . Then angle DAB = 60 ° , an- gle ABD = 30 ° . √4a2 — a2 = a√3 . FIG . 12 . If AB = 2 a , then AD = a , and DB : = DB AB = ... sin 60 ...
Página 41
... triangles . Let ABC be a right- angled triangle , C being the right angle . In what follows , a , b , c , denote the lengths of the sides opposite to the angles A , B , C , respectively . The sides and angles of ABC are connected by the ...
... triangles . Let ABC be a right- angled triangle , C being the right angle . In what follows , a , b , c , denote the lengths of the sides opposite to the angles A , B , C , respectively . The sides and angles of ABC are connected by the ...
Página 44
... triangle is equal to the product of the hypotenuse . and the sine of the ... triangle is equal to the product of the other side and the tangent of the angle ... ABC , right - angled at C , a = 42 ft . , b 56 ft . Find B the hypotenuse ...
... triangle is equal to the product of the hypotenuse . and the sine of the ... triangle is equal to the product of the other side and the tangent of the angle ... ABC , right - angled at C , a = 42 ft . , b 56 ft . Find B the hypotenuse ...
Página 46
... triangle ABC right angled at C , c = 60 ft . , b = 50 ft .; find side a and the acute angles . C = 60 Ft . A b 50 Ft . C FIG . 17 . B α I. Computation without logarithms . b cos A - с 50 = = .8333 . 60 B = 90 ° A. - .. A 33 ° 33'.75 ...
... triangle ABC right angled at C , c = 60 ft . , b = 50 ft .; find side a and the acute angles . C = 60 Ft . A b 50 Ft . C FIG . 17 . B α I. Computation without logarithms . b cos A - с 50 = = .8333 . 60 B = 90 ° A. - .. A 33 ° 33'.75 ...
Página 47
... triangle ABC right angled at C , b = 300 ft . and A = 37 ° 20 ' Solve the triangle . I. Computation without logarithms . B = 90 A 90 ° - 37 ° 30 ' = - 52 ° 40 ' . B C = b cos A = 300 = 377.3 . .7951 - 300 x .7627 = 228.8 . Ο c sin A. 37 ...
... triangle ABC right angled at C , b = 300 ft . and A = 37 ° 20 ' Solve the triangle . I. Computation without logarithms . B = 90 A 90 ° - 37 ° 30 ' = - 52 ° 40 ' . B C = b cos A = 300 = 377.3 . .7951 - 300 x .7627 = 228.8 . Ο c sin A. 37 ...
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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
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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.