Applied mathematics for radio and communication engineers by Carl E. Smith

By Carl E. Smith

Arithmetic, advisor, How-to, Communications, Engineering

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Which in the above example was measured by c and C. The important thing to see, however, is that when these ratios are equal, regardless of the size of the right triangle, the correspond­ ing angles of the two triangles are also equal. The triangles are said to be "similar" triangles. If we are given a voltage V I and the ratio between it and another voltage V 2, it is easy to find the other voltage. For instance, if V I = 10 volts and we know that V 2 is five times as large as VI, then V 2 = 50 volts.

The opposite side grows larger while the adjacent side grow smaller. The result is that the tangent grows larger rather slowly up to 45 degrees but then grows larger rapidly as the angle increases to 90 degrees. In the case of the sine and cosine, only one term in the ratio varied. The student should now inspect a table of trigonometric functions (a brief table is at the back of this book). These functions may be listed as natural sines and cosines in one table 72 APPLIED MATHEMATICS TRIGONOMETRY and natural tangents and cotangents in the other table.

8. This is due to the fact that the sum of the interior angles of a triangle is 180 degrees. Since we are using right triangles, one of these angles equals 90° and hence the sum of the other two angles equals 180° - 90° = 90°. This says that a {3 = 90°, SOll a = 36°52', {3 = 90° - a = 90° - 36°52' = 53°08'. " That is, if one angle increases a certain amount the other angle must decrease the same amount and vice versa. If one side and an angle of a right triangle are given it is possible to find the value of the other sides and angles by means of trigonometry.

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