|
* TRIGONOMETRIC FORMUL'E v y G
<br /> a
<br /> a c c
<br /> a
<br /> b A b A
<br /> C
<br /> L C — C J
<br /> Right Triangle Oblique Triangles
<br /> Solution oU Right Triangles j
<br /> a b a b a a
<br /> 'i r For Angle A. sin =c,,,cos= ,tan= b,cot = a,sec=b, cosec_
<br /> / • e Given/ Required a
<br /> I Q ' !U I b �y `` a, b A, B,c tanA=a= cotB c = as s z
<br /> j _ b �= a 1
<br /> s T as
<br /> a, c A, B, b sin A=Q='aos"B,b aq
<br /> 1 .�✓•' ,� 3. o z 1�..a B, b, a B=90'-A, b =a cot A,a= a r f
<br /> sin A.
<br /> A, b B, a, c B=90°—A,a = b tan A,c= b `
<br /> cos A.
<br /> A,e B, a, b i B=W*-!.A,a =a sin A,b=c cos A,
<br /> Solution of Qblique Triangles /!
<br /> /ru 3 Given Required a sin B
<br /> 16 A' B' a b' e C b — sinA ' c = 180*—�A+B), a = asiA
<br /> sin A
<br /> A, a, b B, c, C sin B= b sn 0
<br /> ¢A,C= 180*—(A+B),c = e i A
<br /> a, b, C A, B, o A+B=180*—C,tan (A-B)=(a—b)tan;
<br /> a sin C a.+ b '
<br /> sin A
<br /> a+b+c — pis- (s—c �-
<br /> V U e jU���,' Z a, b, a A, B, C s= 2 ,sin lA—A/ b e
<br /> sinJB=��l ( C-180*—(A+B)
<br /> ac
<br /> a, b, a Area a= 2 , area
<br /> C ' �'��•�F� /a 1. A, b, c Area area b e sin A
<br /> �7 2
<br /> — a'sin B sin C'
<br /> A,B,C,a Area area = 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope•distance multiplied by the
<br /> Y
<br /> cosi nsof the vertical angle.Thus:slope distance=319.4 ft.
<br /> spe Vert. angle=6*10'. From Table,Page IX s b°101=
<br /> 3 ce3g19,4X. M-818.0a ft.
<br /> �.p�,2 ✓� a'. � 7 c0e a 8869. Horizontal distan �
<br /> 3 51 rq1 Horizontal distance also=Slope distance minus slope
<br /> q distance times (1—ceslne of vertical angle). With the
<br /> q/ �' 4 Y / g, 5 3 '( Qe 1+ same figures as in the preceding eaam'plp,.the follow-
<br /> L-7 L 1 aoataI distauft ing result is obtained.Cosine b°1(Y it-.9868=,0041.
<br /> y� 318:4X.0041=1.31.318.4-1.31=3I&%'ft.
<br /> v!�`F Q T(9'�L '3 WLeathe rtes is Icao
<br /> /O i 1 wn,the horizontal distance is approafma�-fhe slope dist-
<br /> us:
<br /> nee leas the square of the rise divided by twice the slope distance us:rise=14 ft.,
<br /> ope distance-3028 ft. Horizontal distance_3026 1-X 14
<br /> 2 X 3028 x302 g-0,32=902?g it,
<br /> a ?
<br /> f
<br /> e
<br /> j
<br />• n j
<br /> s
<br /> V
<br /> 7 e. -
<br />
|