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<br />�f TRIGONOMETRIC FORMULAE
<br />P J5 B
<br />j- 3 3?-Sr 0 -ate
<br />tau a e a e a
<br />d A
<br />�� ego 3 c b CbA
<br />12,
<br />�•
<br />•�I
<br />I�' •1 /-° po Right Triangle Oblique Triangles
<br />�S / 77 J Solution of Right Triangles
<br />-33. _ pp For Angle A.
<br />sin = e ,cos= e , tan= , cot = a , sec = 8 , cosec =
<br />�# y v Given Required a
<br />a, b A, B , c tan A = -• = cot B, e = a= -j- ' = a
<br />D
<br />b r. as
<br />.l / �f d• s —�-
<br />A, B, b sin A = a - =coo B, b Q
<br />V ae
<br />Y �' :� •- / � „�� � � yea � f _�� I` A' a B, b' C B= 0a a
<br />9. —A, b = a cot$, c= sin A.
<br />o ,
<br />_ y _
<br />�3 A' b B, a, o B=90° a= btanA c= b
<br />' cos A.
<br />�` -��"'�� A,c B, a, b i B=90.°-d,a=ceinA b=ccosA
<br />2,,G Solution of Oblique Triangles
<br />Given Required a ein B
<br />in C
<br />A, B, a b, c, C b = , C = 180°—(A {- B), C = ®;n A
<br />j ✓ sin A
<br />bsin AaeinC
<br />A,a,b B,c,C einB= a rC=180° —(A -1 B),C= sin
<br />-07 Pio ,(a—) +
<br />�w, $ —�. /3 - n_ - .� a b, C A, B, a A { B=184° -.C, tan(A-B)- b tan (A B),
<br />y
<br />� f �. ..� � � � /iy p4 � 61n A
<br />3�
<br />a� Z-/ -)7- � a, b, a A, B, C
<br />0 s a+b+a,sinA-
<br />f,Ca y^� a y ov �
<br />2 -� be
<br />11 „�3 7 -14
<br />vin jB_ ��.•.— �� c=Iso°—(A+B)
<br />/ ac
<br />c S L
<br />to [°o - a, 2
<br />t '� '
<br />-� �j„ 3 /� � p • 7i' '- b c Area
<br />2rZO A, b, a Area area = b e stn A
<br />go -o 2
<br />A, B. C, a Area area = a= sin B sin t7. .
<br />2 sin A
<br />REDUCTION TO -HORIZONTAL
<br />i - Horizontal distance= Slope distance multiplied by the
<br />cosine elthevertical angle. Thus: slope distance =319.4 ft.
<br />s t~6$ m Vert. angle=5° 101. Brom Table, Page fY_ cos 50 1W=
<br />a
<br />9959. Horizontal distance=319.4X.9958=318.09 ft.
<br />ggle Horizontal distance also=Slope distance minus slope
<br />distance times (1 --cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />( Horizontal•distaaee ing result is obtained. Cosine 50101=.9959. j-.p959=.0"j.
<br />319.4X.0041=1.31.319.4 1.31=318 08 ft. i. i -. - When the -rise is known, the horizontal distance is approximately= -the slope dist-
<br />mea less the square of the rise divided by twice the slope distance. Thus: rise=14 it,
<br />�aYope distance=3026 ft. Horizontal distance=SOZ.t�-- 14 X 14
<br />2X302.6
<br />-3$2$-0.32=302211 ti.
<br />.4 MADE IN Il, a. A,
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