## Elements of Plane TrigonometryLilly, Wait, Colman, and Holden, 1834 - 72 pages |

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Elements of Plane Trigonometry, with Its Application to Mensuration of ... William Smyth No preview available - 2017 |

### Common terms and phrases

acute angles angle ACB angle of depression angle of elevation arc AE arc CD arcs AB arithm BC 70 yds BOWDOIN COLLEGE circle constructed cosecant cotangent determine divided equal to radius equation art Expressions feet find AC find the angle find the remaining Geom given side given the side horizontal plane hypothenuse L. T. JACKSON Let the angles line BD line of chords line of numbers logarithm of 100 logarithmic sine manner measure obtain perpendicular plane triangle point F point of division proposed triangle quadrant remaining sides represent the logarithm required the height right angled triangle series of triangles side AB side AC similar triangles sine and cosine station subtracting take the angles tang AE tangent and secant tower triangle ABC fig triangle CDE triangle proposed trigonometry twice the sine whence yards

### Popular passages

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 - A line 27 yards long, will exactly reach from the top of a fort to the opposite bank of a river, which is known to be 23 yards broad ; what is the height of the fort?

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 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 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 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 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 - 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 - Being on the side of a river, and wanting to know the distance to a house which was seen on the other side, I measured...

Page 69 - Prob. 12. How must three trees, A, B, C, be planted, so that the angle at A may be double the angle at B, the angle at B double the angle at C, and a line of 400 yards may just go round them ? Ans.