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" The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5. "
Elementary text-book of trigonometry - Side 158
av Robert Hamilton Pinkerton - 1884 - 176 sider
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New Series of The Mathematical Repository, Volum 5

Thomas Leybourn - 1830
...3*42753753 &calso perform the same operation with the fraction 45*2534534 £c, where the radix is 6. 2. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5. Find the ratio of the sides, and the...
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Problems in the Different Branches of Philosophy: Adapted to the Course of ...

Miles Bland - 1830 - 374 sider
...produced. 3, 4, 5, and the radius of the inscribed circle is known: determine the area of the triangle. 19. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5. Determine the ratio of the sides, and...
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

1836 - 335 sider
...— 4 sin a sin2 ^ ; and explain fully its use in the construction of the Trigonometrical Canon. 64. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5. Find the ratiaof the sides, and the...
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A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms ...

John Hymers - 1841 - 151 sider
...•• ™ «» : АС AB sec В АС 20 100* .-. i- РАС = 'i = 0°. 5729577 = 34'. 22",б4. 37. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 to 5. Shew that its largest angle equals...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845
...of the circumscribing circle, and the three angles. 165. The sides of a triangle are in arithmetic progression, and its area is to the area of an equilateral triangle of the same area as 3 : 5 ; find the ratio of the sides, and the value of the largest angle. 1 66. The...
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A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - 1847 - 80 sider
...Given the base, the vertical angle, and the difference of the sides ; find the remaining angles. 30. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5. Find the ratio of the sides and the...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1852
...where the lines bisecting the angles meet the opposite sides as (a + b)(a + c) (b + c): iabc. 185. The sides of a triangle are in Arithmetical progression,...area is to the area of an equilateral triangle of the same perimeter as 3 : 5 ; find the ratio of the sides, and the value of the greatest angle. 186....
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The Elements of Plane and Spherical Trigonometry

John Hind - 1855 - 328 sider
...circles, it is required to prove that where r„ r„ rt are the radii of the escribed circles. 59. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5; prove that the sides are as 3, 5, 7,...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - 1858 - 232 sider
...a1 + я? cot' ß -x* cot* a 2bxcotß~ ~' Чах coi ß ~ ' ^ ab (a + b) 5t*a-(a + 6)cof/3' ili 56. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 to 5 ; shew that its largest angle equals...
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Plane Trigonometry ...

Isaac Todhunter - 1860
...whose sides are proportional to has its area and the trigonometrical ratios of its angles rational. 8. The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 to 5. Find the ratio of the sides and the...
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