Fundamentals of Practical Mathematics

Cover Fundamentals of Practical Mathematics
Fundamentals of Practical Mathematics
George Wentworth
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8. 38, 72. 1". 11. 40, 36 mi. 14. 75, 400 yd. 138 TRIGONOMETRY Cosine of an Angle. In any triangle the sum of all the angles is 180, so that in a right triangle the sum of the acute angles is 90. Angle B in the figure below is the com- plement of angle A; that is, Z. B is equal to 90 minus Z^4, which is what we mean when we speak of the complement of an angle. The sine of the complement of an angle is called the cosine of the angle, the syllable "co-" standing for "complement. " We write cos A ...for "cosine of angled. " By definition, cos A is the same as sin B, and in this figure b cos^L = - ; c whence ccosA. Table of Cosines. The following short table of cosines of angles may be used with the exercises given on page 139: Angle cos Angle C03 Angle cos 10 0. 9848 40 0. 7660 70 0. 3420 15 . 9659 45 . 7071 75 . 2588 20 . 9397 50 . 6428 80 . 1736 30 . 8660 60 . 5000 90 . 0000 Practical Use of the Cosine. In shoring up the wall BC it is desired to use 20-foot timbers and to have the shores make an angle of 45 with the horizontal.

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