Plane TrigonometryLongmans, Green, and Company, 1906 |
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Page 17
... Tower and Notre Dame Cathedral is 71⁄2 in . What is the distance between those points , the map being drawn to a scale 1 : 20000 ? 8. Make the comparison of angles asked for in Exs . 8 , 9 , 10 , Art . 8 ; Exs . 11 , 12 , 13 , Art . 9 ...
... Tower and Notre Dame Cathedral is 71⁄2 in . What is the distance between those points , the map being drawn to a scale 1 : 20000 ? 8. Make the comparison of angles asked for in Exs . 8 , 9 , 10 , Art . 8 ; Exs . 11 , 12 , 13 , Art . 9 ...
Page 51
... tower , the angle of elevation of the top of the tower is observed to be 60 ° . Find the height of the tower . Let AB be the tower , and P the point of observa- tion . By the observations , - AP 150 ft . , APB = 60 ° . P / 60 150 Ft ...
... tower , the angle of elevation of the top of the tower is observed to be 60 ° . Find the height of the tower . Let AB be the tower , and P the point of observa- tion . By the observations , - AP 150 ft . , APB = 60 ° . P / 60 150 Ft ...
Page 52
... tower , and on a level with its base , the eleva- tion of the top of the tower is found to be 65 ° 40.5 ' . What is the height of the tower ? 5. From the top of a tower 120 ft . high the angle of depression of an object on a level with ...
... tower , and on a level with its base , the eleva- tion of the top of the tower is found to be 65 ° 40.5 ' . What is the height of the tower ? 5. From the top of a tower 120 ft . high the angle of depression of an object on a level with ...
Page 114
... tower at the extremities of the line are 32 ° and 58 ° , the height of the observer's eye being 5 ft . 7. Find the height of a tower on top of a hill , when a horizontal base line on a level with the foot of the hill and in the same ...
... tower at the extremities of the line are 32 ° and 58 ° , the height of the observer's eye being 5 ft . 7. Find the height of a tower on top of a hill , when a horizontal base line on a level with the foot of the hill and in the same ...
Page 115
... tower subtends an angle a at a point on the same level as the foot of the tower and , at a second point , h feet above the first , the depression of the foot of the tower is ß . Show that the height of the tower is h tan a cot B. 13 ...
... tower subtends an angle a at a point on the same level as the foot of the tower and , at a second point , h feet above the first , the depression of the foot of the tower is ß . Show that the height of the tower is h tan a cot B. 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