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<br />TRIGONOMETRIC. FORMU i
<br />o p
<br />a
<br />I g CA
<br />Right Triangle Oblique. Triangles
<br />l Solution of Right 'Triangles — —
<br />u�
<br />For Angie A. sin = , cos c , tan= b , cot a , sec ^ b , cosec o
<br />a
<br />Given Required a z
<br />a, b A, B ,c tan A = b = cot B,:a az = a I'+
<br />a2
<br />77 z
<br />C A, B, b a
<br />S, v
<br />/ '
<br />� A, a B,_ b, c 8=90°—A, b = acotA, c=' a
<br />A, b ' B, a, G B = 90°—A, a _ b tan A, c=
<br />b
<br />i I cos A.
<br />°
<br />c B, a, b B-90— a = e siu A, b = c cos A.,
<br />Solution of Oblique Triangles
<br />Given Rdiauired a sin B a sin C
<br />A B, a b, q C b sin A ; C = 180`--(A j B), G =
<br />A
<br />stn
<br />A, a, b B, c, G' sin B = bsin A a
<br />, Q sin C = 180°—(A } B}, c =
<br />a sin A
<br />C A, B, e A+B=180°— C, tan (A—B)— (a—b) a ' �a +B),
<br />(
<br />l' 4' a'
<br />a sin C
<br />•
<br />_
<br />" a ein A
<br />b, a A, B, C s—a+b+a,sin?A—AI (s—
<br />b)(a—c
<br />sin JB={s—a4% C=180°—(A-+-B)
<br />1
<br />a+b+c
<br />te, b, c Area e = 2 ,area
<br />A, b, c Areab a sin A
<br />Brea
<br />2
<br />as sin B sin 4
<br />4, B, C, a Area Brea =
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />E
<br />e cosine oftheverLcalangle.Thus- slope distance =319.4 ft.
<br />1 d+s 'e Vert. angle= 511Io'. From Table, Page 1Y_ cos 50 1N=
<br />9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />aQ e w Horizontal distance also=Slope distance minus slope
<br />atie
<br />! distance
<br />ve times (1—cosine of vertical angle). With the
<br />r
<br />same fiP ores as in the preceding example, the follow -
<br />Horizontal distance Ing result is obtained. Cosine 5°t0A=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=313.09 ft.
<br />When the -rise is known, the horizontal distance is approximately:—the slope dist-
<br />once less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft,
<br />t
<br />slope distanee=302B ft Harizontal distance=3028— 14 X 14 =3028-0.32=30223 fL
<br />!
<br />2X3028
<br />MADE IN u. 6-A.
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