Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 48
... feet and 672 feet , and their included angle 55 ° 40 ' . ed the distance AB . Requir- Ans . 592.967 ft . B 5. Being on a horizontal plane , and wanting to ascertain the height of a tower , standing on the top of an inaccessible hill ...
... feet and 672 feet , and their included angle 55 ° 40 ' . ed the distance AB . Requir- Ans . 592.967 ft . B 5. Being on a horizontal plane , and wanting to ascertain the height of a tower , standing on the top of an inaccessible hill ...
Page 106
... feet ? 3. How many square yards are whose base is 66.3 feet , and altitude Ans . 41738.49 sq . ft . there in a rectangle , 33.3 feet ? Ans . 245.31 sq . yd . 4. What is the area of a rectangular board , whose length is 12 feet , and ...
... feet ? 3. How many square yards are whose base is 66.3 feet , and altitude Ans . 41738.49 sq . ft . there in a rectangle , 33.3 feet ? Ans . 245.31 sq . yd . 4. What is the area of a rectangular board , whose length is 12 feet , and ...
Page 107
... 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 ...
Page 108
... 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- 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- angle , the angles and sides being de- noted as ...
Page 112
... feet are contained in a plank , whose length is 12 feet 6 inches , the breadth at the greater end 15 inches , and at the less end 11 inches ? Ans . 131 . 3. How many square yards are there in a trapezoid , whose parallel sides are 240 feet ...
... feet are contained in a plank , whose length is 12 feet 6 inches , the breadth at the greater end 15 inches , and at the less end 11 inches ? Ans . 131 . 3. How many square yards are there in a trapezoid , whose parallel sides are 240 feet ...
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following