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acute angles angle of elevation applied base bottom calculated called chords circle circumference complement consequence considered constructed convenient cosecant cotangent determine difference direct distance divided division draw drawn equal equation evident example expressions extent fall feet find the angle given half height hence hill hypothenuse increases known logarithm magnitude manner means measure minute multiply natural numbers object observed obtain opposite parallel perpendicular positive preceding PROBLEM proportion proposed quadrant radius remaining sides represent respectively right angled triangle rules scale secant series of triangles side AB side AC similar sine and cosine solution sought square station substituting subtracting supposed tang tangent third tion tower triangle ABC fig trigonometry twice whence yards
Page 29 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 46 - Ex. 2. From the edge of a ditch 18 feet wide, surrounding a fort, the angle of elevation of the wall was found to be 62° 40'. Required the height of the wall, and the length of a ladder necessary to reach from my station to the top of it. Ans.
Page 47 - ... and 63° 41'. Find the distance of each ship from the fort. 235. From the summit of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column, standing in the horizontal plane, are found to be 30° and 60° respectively.
Page 8 - For this purpose it is divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. The degrees, minutes, and seconds are marked thus ° ' " ; and 9° 18' 16", are read, 9 degrees 18 minutes and 16 seconds.
Page 16 - The COSINE of an arc, is the sine of the complement of that arc, and is equal to the part of the radius comprised between the centre of the circle and the foot of the sine.
Page 48 - ... to be on a level with the place where I stood, close by the side of the river ; and not having room to measure backward...
Page 47 - Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it ; and at each end of this line I .found the angles subtended by the other end and a tree, close to the bank on the other side of the river, to be 53° and 79° 12'.
Page 47 - I measured out for a base 400 yards in a right line by the side of the river, and found that the two angles, one at each end of this line, subtended by the other end and the house, were 68° 2
Page 47 - ... required the altitude of the tower ? Ans. 221-55 feet. EXAM. xi. From the top of a tower, by the sea-side, of 1 43 feet high, it was observed that the angle of depression of a ship's bottom, then at anchor, measured 35° ; what then was the ship's distance from the bottom of the wall ? , Ans.