Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of Computation, Volumen1H. Holt, 1882 - 168 páginas |
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Página 66
... base , we can find the altitude of the triangle im- mediately , and afterwards may find the three required parts of the triangle from the altitude . CASE III . Given the three sides . THEOREM III . In a triangle the square of any side ...
... base , we can find the altitude of the triangle im- mediately , and afterwards may find the three required parts of the triangle from the altitude . CASE III . Given the three sides . THEOREM III . In a triangle the square of any side ...
Página 69
... base of a parallelogram is 13 , each side is 6 , and its lesser diagonal is 12. Find its angles . 5. If the sides of ... base . Prove Base = √2p + 2q2 - 4r3 . Р r 8. Given the three medial lines r , r ' , r " of a triangle ; find the ...
... base of a parallelogram is 13 , each side is 6 , and its lesser diagonal is 12. Find its angles . 5. If the sides of ... base . Prove Base = √2p + 2q2 - 4r3 . Р r 8. Given the three medial lines r , r ' , r " of a triangle ; find the ...
Página 73
... base into the altitude . Now in the figure , Altitude hb sin y . Therefore , a being the base , Area tahab sin y . - Q.E.D. Cor . 1. If two triangles have two sides of the one respectively equal to two sides of the other , and the ...
... base into the altitude . Now in the figure , Altitude hb sin y . Therefore , a being the base , Area tahab sin y . - Q.E.D. Cor . 1. If two triangles have two sides of the one respectively equal to two sides of the other , and the ...
Página 74
... base . Let us put a , b , the parallel sides ; m : 1 - m , the ratio in which the non parallel sides , and there- fore the altitude , is divided by the dividing line ; k , the length of the dividing line . The unknown quantities of the ...
... base . Let us put a , b , the parallel sides ; m : 1 - m , the ratio in which the non parallel sides , and there- fore the altitude , is divided by the dividing line ; k , the length of the dividing line . The unknown quantities of the ...
Página 82
... base line from which the angles a , ß , y , etc. , are counted ; AB , any side of the polygon ; a , its length ; a , the angle which AB makes with X. Draw OY perpendicular to OX , and let PQ be the projection of AB upon OY . IAB will ...
... base line from which the angles a , ß , y , etc. , are counted ; AB , any side of the polygon ; a , its length ; a , the angle which AB makes with X. Draw OY perpendicular to OX , and let PQ be the projection of AB upon OY . IAB will ...
Términos y frases comunes
algebraic signs angle AOB angle XOM axes base circle circumference coefficients compute cos² cos³ cosec cosine cotangent distance divided equal example EXERCISES expression find the angles find the remaining find the values formulæ given gives Hence hypothenuse imaginary unit intersect latitude line OX measure metres negative nth roots obtain opposite angles parallel parallelogram perpendicular polar triangle pole polygon positive direction preceding problem quantities radius rectangular co-ordinates right angle right triangle roots of unity secant sin a cos sin a sin sin² sine sines and cosines Solution spherical triangle spherical trigonometry squares straight line substituting subtract supplementary angles suppose three angles three rectangular planes three sides tion trapezoid trigonometric functions trihedral angle vertex zero
Pasajes populares
Página 66 - 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 139 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 132 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.
Página 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 66 - IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle...
Página 105 - ... the modulus of a product is equal to the product of the moduli of the factors.
Página 43 - At the top of a tower, 108 feet high, the angles of depression of the top and bottom of...
Página 73 - The area of a triangle is equal to half the product of any two of its sides multiplied by the sine of the included angle, radius being unity.