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TRIGONOMETRIC FORMULIE
<br />r
<br />}3 B B
<br />o a c a c a.
<br />r' g : A b C b C
<br />C
<br />j Right Triangle Oblique Triangles ,
<br />Solution's of Right Triangles
<br />For Angle A. .sin = a , cos = b , tan = a ,' cot = b , see = , cosec =
<br />c c b a b a
<br />.Given Required �y 2
<br />a, b A, B ,c tan A = b = cot B, c = a2 -f- 2 = a 1 I az
<br />a, c' A,-B,b sinA=E=cosB,b=�(c+a
<br />A, a B, b, c B=90°=A, b =. a cotes, c= a
<br />sin A.
<br />I • A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />c B, a, b I B = 90°—A, a = c sin•A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required a sin B a sin C
<br />A, B, a b, c, C b = sin A ' C 180°—(A + B), c =
<br />• sin A
<br />b sin Aa sin C
<br />,:. d,'a,;b Ac, C sinB= a ,0=180°—(A+B),c= sin
<br />a, b, C A, B, c A+B=180°— C. tan i (A—B). (a—b) tan z (A+B)�
<br />a -E• b
<br />c=
<br />a sin C
<br />sin A
<br />a+b F o I
<br />a, b, c , ' A, .B,' C s = 2 ,sin 3A= V, '
<br />sin'-, B=�(s—a)(s�) , C=180°—(A+B)
<br />ac
<br />a, b, c Area s= a+2+c,, area = s(s—a) (s—) (a—o
<br />A, b, a Area b e A
<br />area = 2 t '
<br />4 A, B, C, a Area area = W sin B sin C
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />1 Horizontal distance =Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />o4e a�StQTce Vert. angle= 50 101. From Table, Page IX. cos 50 10/=
<br />9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />S, 4e ,e Horizontal
<br />distance
<br />letstance minus ltncemes(lccoine of vertical angle).Withthe
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 5° 101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31.319.4-1.31=318.09 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 it..
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X 14 =302,6-0.32=30228 ft
<br />2 X 302.6
<br />Auue lM U. a. A.
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