 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...  Plane Trigonometry - Page 202by Daniel Alexander Murray - 1906Full view - About this book
 | Queen's University (Kingston, Ont.) - 1896 - 898 pages
...+В+С=я, tan 4+tan B+t&n С =ta,nA tan B tan ('. (6) J(a+6)coeC=a+6+c. 4. (a) If p be the perimeter of a regular polygon of n sides inscribed in a circle, and P be the perimeter of the corresponding polygon circumscribing the circle ; and also if plt P! be the... | |
 | James William Nicholson - Trigonometry - 1898 - 204 pages
...equal to one.half the product of its diagonals into the sine of their included angle. 12. Show that the area of a regular polygon of n sides inscribed in a circle whose radius is R, is one.half the product of n by the square of R into the sine of - (360°). MISCELLANEOUS... | |
 | Daniel Alexander Murray - Plane trigonometry - 1899 - 226 pages
...indefinitely diminished is 1, ie tan 6 = 6, very nearly. 12. Find the area of a regular polygon of re sides inscribed in a circle, and show, by increasing...which a building 50 ft. wide will subtend an angle of ?>'. (6) A church spire 45 ft. high subtends an angle of 9' at the eye. Find its distance approximately'... | |
 | Daniel Alexander Murray - Plane trigonometry - 1899 - 350 pages
...0, very nearly. (6) Show that the limit of an when 0 is indefinitely diminished is 1, ie tan 0 = 0, very nearly. 12. Find the area of a regular polygon...expression for the area of the circle may be obtained. 18. (a) Find the distance at which a building 50 ft. wide will subtend an angle of Si'. (6) A church... | |
 | 1904 - 386 pages
...calculation and verify it by a drawing made to scale. NB ^5 = 2'236. ' (40) 57. Write down an expression for the area of a regular polygon of n sides inscribed in a circle of given radius, and deduce from it the expression for the area of a circle of given radius. (30) 58.... | |
 | Walter Gustav Borchardt - Trigonometry - 1904 - 206 pages
...4 . / bd sin •= sin ^ sm -= sin -= . ¿ \ s M л а REGULAR POLYGONS. 167. To find the radius and area of a regular polygon of n sides inscribed in a circle. Let AB (= a) be one of the sides of the polygon and O the centre of the circumscribing circle. Draw... | |
 | 1906 - 502 pages
...not very often attempted, but when taken in hand the relation was usually correctly inade out. Q. 58. Find the area of a regular polygon of n sides inscribed in a circle of radius r, and deduce the area of the circle. Find the ratio of the area of a circle to that of a... | |
 | Education - 1914 - 914 pages
...to questions 1 to 5 shall count 10 each; to question 6, 14; and to questions 7 and 8, 18 each.] 1. Find the area of a regular polygon of n sides, inscribed...without limit, how the expression for the area of a circle may be obtained. 1 1 2. If sin A= , and sin B = . show that one value of A + B if 45°. V5,... | |
 | Geometry - 100 pages
...rhombus is equal to one-half the product of its diagonals. Area of the rhombus = - ACXBD Theorem 6 The area of a regular polygon of n sides inscribed in a circle of radius R, is given by the formula: r2 sin72° Theorem 7 The area of a regular polygon of n sides... | |
 | 1874 - 748 pages
...— c) a + Ь + с) (b + с - a) (3) (a + b) cos С + (Ь + с) cos A + (с + a) cosB = a+ * + c. 11. Find the area of a regular polygon of (n) sides inscribed...expression for the area of the circle may be obtained. 12. In a triangle ABC, given AC = 150 feet, BC = 200 feet, AB = 250 feet ; find all the angles of the... | |
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