Plane TrigonometryLongmans, Green, and Company, 1906 |
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Page 11
... perpendicular ? Calculate the following ratios , viz .: perpendicular hypotenuse base hypotenuse ' perpendicular base base hypotenuse hypotenuse perpendicular base perpendicular What are these ratios in a triangle whose base is 8. ] 11 ...
... perpendicular ? Calculate the following ratios , viz .: perpendicular hypotenuse base hypotenuse ' perpendicular base base hypotenuse hypotenuse perpendicular base perpendicular What are these ratios in a triangle whose base is 8. ] 11 ...
Page 12
... perpendicular 21 ft .; for the triangle whose hypotenuse is 2.9 in . , and perpendicular 2.1 in . Compare , if possible , the angles in these triangles . 9. Incommensurable quantities . Approximations . If the side of a square is one ...
... perpendicular 21 ft .; for the triangle whose hypotenuse is 2.9 in . , and perpendicular 2.1 in . Compare , if possible , the angles in these triangles . 9. Incommensurable quantities . Approximations . If the side of a square is one ...
Page 18
... perpendicular to another line , each of the angles made at their intersection is a right angle ; ( 2 ) All right angles are equal to one another . In some geomet- rical propositions angles are compared , and one angle is shown to be ...
... perpendicular to another line , each of the angles made at their intersection is a right angle ; ( 2 ) All right angles are equal to one another . In some geomet- rical propositions angles are compared , and one angle is shown to be ...
Page 20
... perpendicular are 30 ft . and 45 ft . respectively . 5. Same as Ex . 2 , for a right - angled triangle whose hypotenuse is 60 ft . and base is 45 ft . 6. Same as Ex . 2 , for a right - angled triangle in which the base is 50 ft . and ...
... perpendicular are 30 ft . and 45 ft . respectively . 5. Same as Ex . 2 , for a right - angled triangle whose hypotenuse is 60 ft . and base is 45 ft . 6. Same as Ex . 2 , for a right - angled triangle in which the base is 50 ft . and ...
Page 21
... perpendicular PM to the other line . The three lines AP , AM , MP , can be taken by twos in three different ways , and hence six ratios can be formed with them , namely : MP AM MP AM AP AP AP -9 AP AM MP AM MP It is shown in Art . 13 ...
... perpendicular PM to the other line . The three lines AP , AM , MP , can be taken by twos in three different ways , and hence six ratios can be formed with them , namely : MP AM MP AM AP AP AP -9 AP AM MP AM MP It is shown in Art . 13 ...
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Common terms and phrases
A+B+C acute angle algebraic centre CHAPTER circumscribing computation cos² cosec cotangent deduced denoted Derive diedral angle draw equal equator EXAMPLES expression figure Find the distance formulas geometry given Hence hypotenuse included angle inscribed circle intersection latitude law of cosines law of sines length logarithms mantissa mathematics meridian method NOTE number of degrees number of sides opposite perpendicular plane triangle Plane Trigonometry polar triangle pole positive quadrant radian measure radii radius regular polygon relations respectively right angles right triangles right-angled triangle secant Show sides and angles sin² solid angle solution Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tables tan² tangent terminal line three angles tower triangle ABC trigono trigonometric functions trigonometric ratios π π
Popular passages
Page 52 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Page 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 108 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - The area of the surface of a sphere is four times the area of a great circle.
Page 108 - 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 72 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 62 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area, F THE RIGHT TRIANGLE.
Page 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 200 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Page 202 - Find the area of a regular polygon of n sides inscribed in a circle, and show, by increasing the number of sides of the polygon without limit, how the expression for the area of the circle may be obtained. 13. (a) Find the distance at which a building 50 ft. wide will subtend an angle of 3'. (6) A church spire 45 ft. high subtends an angle of 9