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Soy TRIGONOMETRIC FORMULAE -7
<br /> L7LI
<br /> 3z' B s B
<br /> 3.9g a c c
<br /> _----
<br /> :ja a
<br /> 9 z-•i- ,
<br /> A C
<br /> 1 pm b. o b C b
<br /> 'j')ilangle Oblique Triangles
<br /> Solution of Right Triangles
<br /> Aadi.. Ab a b o
<br /> For , sin = e ,coo= o—,tan= b.cot= a—,see=b, cosec=
<br /> 33i
<br /> Required a
<br /> A, B,e tan. = cot B,c = a =a 1 a ; .
<br /> ?? T b T q
<br /> J t h�o��O
<br /> 3 /!/v p a, Q ?iB, b siaA=Q=cosB,b=%/ o Fa
<br /> /J o ,
<br /> B, b, o _B=90°—A,b=a cotA,e= a
<br /> ' J
<br /> sin A.
<br /> G�,tI' r A b B,a, c B=90°—A,a= b tan A,o= ' 1
<br /> J cos A.
<br /> t :
<br /> AP o B,a, b B=90°d,a=-o sin A,b=ocos A,
<br /> _ Solution of Oblique Triangles
<br /> ' (liven Required a sin B
<br /> d, B,a b, o, C b = sinA ' C= 180°—(A+B),c ='asinC
<br /> V sin A
<br /> P ?
<br /> "A, a, b B,c, C sin B= b sin ASC= 180'—(A+B),c = a sin C
<br /> a sin A
<br /> a, b, C A,B,e A+B=180°—C,tan#(A—B)= a—b tan (A�B)
<br /> ,
<br /> _ a sin C a + b
<br /> sin A
<br /> \ \\\\1 { a b
<br /> b, a A, B, C 8= + +e,sinA=
<br /> 2 be
<br /> sl zPn' 4 sin+)B=V a—aa(Q ,C=180'—(A+B)
<br /> z a+b+o
<br /> v 5' a+ b, o - ea 8= 2 , area = e s—a 8— s—o
<br /> ' 4 A, b, a Area b e sin A e
<br /> area = 2
<br /> as sin B sin C
<br /> 3 7 ` A,B,C,a Area area = 2 sin A
<br /> r " p: REDUCTION TO HORIZONTAL
<br /> Horizontal distance-Slope distance multiplied by the
<br /> cosine of the vertical angle.Thus:slope distance=819.4 It.
<br /> • 1� Vert. angle=b W. From Table,Page m cos 501W=
<br /> 9969. Horizontal distanoe=819.4X.9869=SI&09 ft.
<br /> Ap41e p� Horizontal distanoe also=Slope distance minus slope
<br /> distance times (1-cosine of vertical angle). With the
<br /> same figures as in the preceding example,the fonow.
<br /> [\ti Horizontal distance ing result is obtained.Cosine b°1W-.9869.1-.9868=.004i.
<br /> 819.4X.0041:=1.81.819.4-1.81=81&O9 ft.
<br /> When the rise is known,the horizontal distance is approximately:-the slope dist-
<br /> �ti ance less the square of the rise divided by twice the slope distance Thus:rise=l4 ft.,
<br /> slope distance-302.6 ft. Horizontal distaaee=802.9- 4X 14-8=6-p,82=802.28 ft.
<br /> 2 X 802.9 _
<br /> MAN IN U.S.A.
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