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<br />j TRIGONOMETRIC FORMULAE
<br />t B B B
<br />c a ° a c a
<br />b 'CA�b OA b `C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angled sin = , cos = a , tan = b , cot = ,sec = b , cosec =
<br />(fiven Required a
<br />a, b; A,B,e, tanA=b=cotB,c= a2 2=a 1 { a2
<br />i
<br />x
<br />q, o' A, B, b sin A = o = cos B, b — \/ (c a (c—a) = c I_E_
<br />s
<br />B,, b, e . B=900—A, b = a cotA,.a= a
<br />stn A.
<br />A, b B, a, e. B = 90°—A, a = b tan A, o= b
<br />' cos A.
<br />A, c. B, a, b B = 90°—A, a = e sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />A, B, a b, c, C b sin A ' C = 1807—(A + B), c = sin Al
<br />e b sin A 1$0°—(A a sin C
<br />A, a, b B, e, C sin B= a ,C = } B), c = sin A
<br />a, b, O A, B, e A+B=180°— C; tan '-2 (A—B)= (a—b).tan $ (A+B)
<br />B)�
<br />a -1- b
<br />�c^asin C
<br />sin A
<br />+b+
<br />a, b, c A, B, C s = 2 ,sin jA=AI b c '
<br />sing= (s—a)1s—o C=180°—(A+B)
<br />ac
<br />a+b+c
<br />a, b; "c Area s= , area =s(T_1 (s— s—c
<br />A; b, c Area area = basin A 2
<br />a2 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 />cosine of the vertical angle..Thus: slope distance =319.4 ft.
<br />_ tiarpe Vert. angle =5° 101. From Table, Page IX. cos 51101=
<br />a ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />g1oQ ngle Horizontal distance also=Slope distance minus slope
<br />1' a distance times (1—cosine of vertical angle). With 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 />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 />slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =3026-0.32=302.28 ft.
<br />2 X 302.6
<br />YnDE 1N U.S. M
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