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<br />- - -- . ,l to v • ...
<br />TRIGONOMETRIC FORMULAE . -•
<br />`„;kms' T- / '� G.L fTG/ YJ • ' Y,
<br />», c
<br />:a; Foa c a c a
<br />b C �b C f
<br />` Right Triangle Oblique Triangles
<br />�• - ` Solution of Right Triangles
<br />i a b a b c e
<br />_.r Angle A. sin = c , cos = c , tan= b , cot = a , sec = L ,; cosec = —
<br />1� a
<br />Given Required z
<br />a,b A, B ,c tan A = =cot B, c = a2 ' = a 1 { —
<br />b �/a=
<br />all
<br />Y� a, c A, B, b sin A=c =cos B,b=%/-F
<br />(ca)(c—a=c�1—Qi
<br />Y ! A, a B, b, c B = 90°—A, b = a cot d, c =
<br />{ _ sin A.
<br />�, •b B, a, c B = 90°—A., a = b tan A, e. = b
<br />cos A.
<br />4
<br />A, e,-• B, a, b B=90°—A,a=csin A,b=ccos A,
<br />_, Solution of Oblique Triangles
<br />Given Required a sin Ba sin C
<br />^ rA, B a` b, c> Cb sin A ' C = 180°—(A I B), c = sin A -43
<br />` b sin A a Bin C
<br />M.. `,. _ �a b• B c Gr sinB= a ,C=180°—(A f B),o= sin
<br />'.r• c :F , tt+ a b, C A, B, c A (8=180°— C, ten ij (A—B)= (a—b) tan s (A } B)
<br />S asin C a + b
<br />ein A
<br />alb}eI
<br />a, b, c A, B, C .,in s_ 2 ,�A=N b e
<br />Bin JB=- 1(s—a s—e), C=180°—(A+B)
<br />ac
<br />j a�b{c
<br />a, b, c Area s= 2 ,area =
<br />A, b, c Areaarea b.e sin A
<br />= 2
<br />as sin B sin C
<br />B, C, a Area ere. = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 it.
<br />stat'ce Vert. 959angle=b° 10. From Table, Page 1X cos 5'1(Y=
<br />' m 9. Horizontal distance=319.4X.9959=318.09 ft.
<br />S`o0e ArQle a Horizontal stance timeSt(leco ne oflso=lope vertic�alance angle).�nus Withlope the
<br />same figures as in the preceding example, the follow-
<br />Horizontal distance ing result is obtained. Cosine 5° 10'—.9959.1—.9959=.0041.
<br />i 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 ft.,
<br />+ : - �', l01 e°-distaif a=3ft6 ft. Horizontal distance=3020— 14 X 14
<br />2 X 3026 .
<br />MADE IN U.S.A. I
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