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� t �� yah' wit c .eL,7t
<br /> L L
<br /> 9. 3 -S 3 T1 I 0 TRIC F6�uL E
<br /> t .ZL B5B rw B
<br /> P7 9 v /y;al,.� i 7 4
<br /> 4.. �t' b3 C A C A t t 9j- 5r
<br /> b
<br /> 'Right Triangle Oblique Triangles Z, Z
<br /> Solution of Right Triangles
<br /> +� • ! f ' 7 Y` For Angle A. sin =a cos= b tan= a b o 0
<br /> 0 ' e ' b 'cot= a,sZC=b. cosec= a
<br /> (liven Reiluired I
<br /> 3 1' a b A, B;c tanA=a= ca c = a=+ _ = a 1 {
<br /> J
<br /> ' / S 1 Z g q • a, c A, B, b sin A=c =cos B,b=%/(c+a (o—a)
<br /> S e i
<br /> 69
<br /> Lf a A,a B, b, c B=90°—A,b =a cotA,c= cin A.
<br /> 7
<br /> � r � 4 -54 A, b B,a, c B=90°—A,a = b tan A,c= b
<br /> -
<br /> i � l con A. J'ts
<br /> r
<br /> -- �7 A,c B, a, b I B=90°—A,a=c sin A,b=c cos A, 4/_ -
<br /> �7 S - Solution of Oblique Triangles
<br /> 1 Given 4 Required
<br /> d, B,a b, c, C b =s n d 'C =180°—(A } B), c =a ain C
<br /> sin A
<br /> f' $ Q A, a, b B,e, C sin B= b sign A C,= 180°—(A-r B),e = sin A
<br /> b, C A, B, c A+B=180°—C,tRn z(A—B)= a—b tan (A+B)
<br /> asin0 a b
<br /> 7 7 G a o =
<br /> �� ?_ sin A `4• v
<br /> ti _ s
<br /> c 6 1' ✓ :, y .L / d6 bo A, B"C s=� ,cin v
<br /> A=�s bo
<br /> 93 4.!S r '
<br /> (8—aH8 c
<br /> 1
<br /> sin ,C=180°--(A+B)
<br /> v ac
<br /> b, c Area s=a+b+c, area = s(a—a a— s---e
<br /> 2
<br /> 7 " G A,b, c Area area = b c sin A
<br /> �_ 2
<br /> 6' ¢ �• "- � / a=sin B sin C 3.�✓`
<br /> ti�6 _^ a pi+ t d,B,C,a Area area = 2 sin A Z
<br /> ` ----- `--?^ 3 REDUCTION TO HORIZONTAL
<br /> G '4 l C Herizontal distance=Slope distance multiplied by the' 1 e cosine of the vertical angle.Thyro V%e distance=318.4 it.
<br /> Vert. angle=6'W. From Table, age IX.cos ti°lw=
<br /> ea 8859. Horizontaldistance=318.4X.9968=313.098.
<br /> �' .- g �' ✓ -, ✓t`9 5104 A9gle a Horizontal distance also=Slops diata/ce minus slope
<br /> 1 I t y r qe distance titres(1-cosine of vertieal angle). With the -. .
<br /> same fignres.as in the preceding example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine b°1!'=•9968.1-,9951:=.W41.
<br /> 9.4X.9041=1.31.319 4-1.31=815 N ft
<br /> 31
<br /> When the rise is known,the horizontal dlstlance is appeadmately:-the slope dist
<br /> > ) f ! ante less the square of the rise divided by twbas the slope 4netance. Thus:rise=l4 ft.,
<br /> -+ slopedistanoe-3neft. Horizontaldbtanm-mLo-- L&K-4LO-0.32=902.28ft.
<br /> .MASS IN U.S.A.
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