Mathematics for Agricultural Students

Cover Mathematics for Agricultural Students
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With C as center and with CA as radius describe an arc cutting BC at E and BC produced at D. Draw AE and AD. BAD is a right triangle with the angle AEC equal to The angle EAB is equal to Draw EK perpendicular to AE.
K FIG. 36.
The triangles BEK an4 BAD are similar. Hence AD AE a + - = tan AE EK 2 BD _ AD BE ~ EK Since BD = a + b, and BE = a b, a + b _ tan J (a + a b tan \ (a cot (D 57] THE CIRCULAR FUNCTIONS 107 which is known as the law of tangents. Since a + /3 + 7 = 180, 2 2' The law of tang
...ents may be used instead of the law of cosines for solving triangles in which two sides and the included angle are given.
ILLUSTRATION : Given a = 337. 6 feet b = 213. 5 feet 7 = 27 16' to find c, a and |8.
Solution: tan $( - |8) = CI ^- tan \(a + j8) a + 6 a - 6 = 124. 1 a + b = 551. 1 J(a + j8) = 76 22' log (a - 6) = 2. 0938 log tan |(a + 0) = 0. 6152 log (o + 6) = 2. 7413 log tan |(a - 0) = 9. 9677 - 10 i( _ 0) = 42 52' a = 119 14' /8 = 33 30' Find the value of c by using the law of sines, b sin 7 c = sin |8 log 6 = 2.


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