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<br />TRIGONOMETRIC FORMULtE
<br />i
<br />B B
<br />I <c a c a c a
<br />b, C Afb C A b G
<br />Right -Triangle Oblique Triangles
<br />Solution of Right 'Triangles' -'
<br />For Angle A. sin-= a , cos = b , tau = a b. , cot = b , sec = cosec = a
<br />c a a b a
<br />Given- , Required
<br />bX
<br />a, b A, B ,e tan -A = h = cot B,
<br />a, c A, B, . ba
<br />sin A = a = cos B, b`= �✓ (c �a) (c—a} = c �J 1— 02
<br />A, a B, b, c B = 90°--A, b = a cot A, c = a
<br />sin A.
<br />A, b B, a, c B = 90°-A, a = b tan A, o = b
<br />A.
<br />A, c B, a, b B=90°—A, a = e sin -A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required' a sin B -
<br />A, B, a b, c, C' b — sin. A ' C = 180°—(A + $), c = sin 11
<br />A, a, b B c, C sBb sin Ain = , a sin C
<br />a C = 18D°—(A } B), c sin A
<br />u, b, C A, B, c A-}-8-180°— C, tan I (A—B)= (°—b) tan z (A+B),
<br />a+b
<br />- a siri C
<br />in A
<br />a, b, c A, B, C s=a+2+
<br />sin !R=
<br />ae
<br />a, b, a Areas=a+2+e, ares = v(s a} Co— ) (y—c)
<br />A, b, e Areab c sin A
<br />area = 2
<br />A, B, C, a Area area = a' sin B sin G'
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distanec=Slope distance multiplied -by the
<br />1 cosine of the vertical angle. Th us: sl ope distance =319. tit.
<br />taz ce Vert. angle=50 101. From Table, Page IX. cos Sa 101=
<br />Oe atis °m 9955. Horizontal distance=319.4X.9959=319.09 ft.
<br />oto An to tz Horizontal distance also=Slope distance minus slope
<br />I `e distance times (1—cosine of vertical angle). With -the
<br />1 same figures as in the preceding example, the follow -
<br />Horizontal distance Ing result is obtained. Cosine 5° IO'=.9959..1=.9959=.0041.
<br />_ 919.4X.0041 =1.31. 319.4-1.31=313A9 ft.-
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=302.6 ft. Horizontal distance=302.8— 14 X 14 =302-6-0.32=302.28 ft.
<br />2 X 302.5
<br />MADE IN U,B. A.
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