## Plane and Spherical Trigonometry |

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Algebra angle of elevation arc degrees arithmetic C/sin Check circle common logarithm complex number compute construct the triangle cos2 cosecant cosh cotangent coterminal diedral directed line draw equal EXERCISE figure Find the area Find the distance Find the height formulas fourth quadrant Geometry Given Hence hour angle included angle isosceles triangle law of cosines law of sines less than 45 log product log quotient logarithms mantissa Observe obtain opposite angle polar triangle pole polygon positive or negative principal value Prove quality unit radius reciprocal right angles right triangle secant second quadrant sin2 sinh solid angle solution Solve sphere spherical angle spherical degrees spherical excess spherical radians spherical triangle Spherical Trigonometry subtended tan2 tangent three sides tower triedral angle trigonometric lines trigonometric ratios vector vertex vertical

### Popular passages

Page 142 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively.

Page 75 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.

Page 155 - If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line of the plane, and its intersection with that line is joined to any point of the perpendicular, this last line will be perpendicular to the line of the plane. Let AP be perpendicular to the plane MN...

Page 78 - 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.

Page 149 - It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle.

Page 19 - ... down it is 28°. The inclination of the plane is 7°. Find the height of the tower. 10. From the top and bottom of a castle which is 75 ft high the angles of depression of a ship at sea are 19° and 15° respectively. Find the distance of the ship from the bottom of the castle. 11. A monument 70 ft. high and a tower stand on the same horizontal plane. The angle of elevation of the top of the tower at the top of the monument is 20° 40' 12" [20.67°], at the base of the monument it is 53° 31'...

Page 18 - ... the angle to be 30°. Find the height of the tree and the breadth of the river, if the two points of observation are in the same horizontal line at the base of the tree.

Page 173 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...

Page 174 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 88 - ... and the shorter diagonal is 16 ft. Find the area. 189. The acute angles of a rhombus are each equal to 60°, and the longer diagonal is 108 yds. Find the area. 190. Two vessels start at the same time from the same place, and sail, one due north, the other due east, at the rates of 6 and 8 mi. per hour respectively. How far apart will they be at the end of 6 hrs. ? 191. What distance will a man save, if, instead of walking along the sides of a rectangular field 640 yds. long and 480 yds. wide,...