By Carl E. Smith

Arithmetic, consultant, How-to, Communications, Engineering

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Lf C is the hypotenuse with A and B the two sides, then + B2 = = VIOO = 10 Resultant =hypotenuse = Geometric sum of Ao+~A=altitude=side C = VA2 57 (1) Applying this basic principle of geometric addition to the above ,t- '". J I C :lie> FIG. -Semicircular ·protractor. (forces). The law states that the resultant of two vectors (forces) which act at any angle upon a rigid body, or point, is represented in magnitude and direction by the diagonal of a parallewgram, the 1 The vertical bars placed on both sides of A and B are used to denote magnitude only of the quantity between them.

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.

A. Altitude = 40. b. Altitude = 5. Base = 30. 66. Find the hypotenuse. Find the hypotenuse. c. Altitude = 5. d. Altitude = 18. 07. Hypotenuse = 30. Find the base. Find the base. e. 3. j. Base = 678. 7. Hypotenuse = 843. Find the altitude. Find the altitude. 2. In each of the following examples, find the resultant vector and state in which quadrant it lies. The directions of the vectors are along the x and y axes as shown in Fig. 20. , on a large sheet of paper, will help you to understand the problem clearly and solve it correctly.