Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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... feet high , will it subtend an angle of 31 ° 17 ' 12 " ? 3. Required the height of a hill D above a hor- izɔntal plane AB , the dis- tance between A and B being equal to 975 yards , Ans . 329.114 ft . D and the angles of elevation at A ...
... feet high , will it subtend an angle of 31 ° 17 ' 12 " ? 3. Required the height of a hill D above a hor- izɔntal plane AB , the dis- tance between A and B being equal to 975 yards , Ans . 329.114 ft . D and the angles of elevation at A ...
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... feet . Ans . 663 . 3. Find the area of a triangle , in square yards , whose base is 49 , and altitude 25 feet . Ans . 68.7361 . Second Case . When two sides and their included angle are given . Let ABC represent a plane tri- angle , in ...
... feet . Ans . 663 . 3. Find the area of a triangle , in square yards , whose base is 49 , and altitude 25 feet . Ans . 68.7361 . Second Case . When two sides and their included angle are given . Let ABC represent a plane tri- angle , in ...
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... feet and 21.25 feet , and their included angle 45 ° ? Ans . 20.8694 . LEMMA . To find half an angle , when the three sides of a plane tri- angle are given . 97. Let ABC be a plane tri- C angle , the angles and sides being de- noted as ...
... feet and 21.25 feet , and their included angle 45 ° ? Ans . 20.8694 . LEMMA . To find half an angle , when the three sides of a plane tri- angle are given . 97. Let ABC be a plane tri- C angle , the angles and sides being de- noted as ...
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... feet ? Ans . 2.123472 ft . To find the area of a circle . 105. From the principle demonstrated in Book V. , Prop ... feet ? diameter Ans . 1.069016 . 3. What is the area of a circle whose circumference is 12 feet ? Ans . 11.4595 . To ...
... feet ? Ans . 2.123472 ft . To find the area of a circle . 105. From the principle demonstrated in Book V. , Prop ... feet ? diameter Ans . 1.069016 . 3. What is the area of a circle whose circumference is 12 feet ? Ans . 11.4595 . To ...
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... feet , and each side of the base 3 feet . Ans . 90 sq . ft 2. What is the entire surface of a right pyramid , whose slant height is 15 feet , and the base a pentagon , of which each side is 25 feet ? Ans . 2012.798 sq . ft . To find the ...
... feet , and each side of the base 3 feet . Ans . 90 sq . ft 2. What is the entire surface of a right pyramid , whose slant height is 15 feet , and the base a pentagon , of which each side is 25 feet ? Ans . 2012.798 sq . ft . To find the ...
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AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence