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Pàgina 61 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Pàgina 105 - By a logical presentation of principles to inspire confidence in the methods of infinitesimal analysis; 2. By numerous problems to aid in acquiring facility in applying these methods ; 3. By applications to problems in physics and engineering, and other branches of mathematics, to show the practical value of the calculus.
Pàgina 62 - B)' (51) 116. In any triangle, the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle.
Pàgina 68 - Construct a triangle, having given two sides and the angle opposite one of them (a, b, /A).
Pàgina 9 - A unit of plane angular measurement equal to the angle at the center of a circle subtended by an arc equal in length to the radius.
Pàgina 28 - ... foot of the post is 8° 32' 15". Calculate the height of the telegraph post and its distance from the observer. 13. A man in a balloon, when it is one mile high, finds the angle of depression of an object on the level ground to be 35° 20', then after ascending vertically and uniformly for 20 min., he finds the angle of depression of the same object to be 55° 40'. Find the rate of ascent of the balloon in miles per hour. 14. A man observes the elevation of a mountain top to be 15°, and after...
Pàgina 55 - The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.
Pàgina 46 - CD is drawn from the vertex of the right angle to the middle point of AB, angle ACD equals 60°.
Pàgina 28 - What is the height of a flagpole if at a horizontal distance of 200 feet from the foot of the pole the angle of elevation of its top is 19° 28
Pàgina 105 - Its object is threefold : ( 1 ) to inspire confidence in the methods of infinitesimal analysis ; (2) to aid in acquiring facility in applying these methods ; and (3) to show the practical value of the calculus by applications to problems in physics and engineering. An Elementary...