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<br />1 r�! ikwoNOMETRIC FORMUL&
<br />.'Right Triangle � Oblique Triangles
<br />Solution of Right Triangles
<br />L 2�' j
<br />I g a 4 s Icor An Ie A. On = a b a b a c.
<br />1 f� fir' ' �r j a g c ,cos — c ,ten = b ,cot = ,sec = b , cosec=,
<br />(O f � �
<br />'` t}tveli , Required a
<br />A, B ,e tan A = b , cot B, a d2 + s. = a
<br />C
<br />a, c A, B, b ` ain A = = coa B, b
<br />A, a B,'90°—A; b= cot A, c a
<br />. ?d�0? i r sin.A
<br />1 / /. c iB 90°—A, a = b tan A,
<br />cos A
<br />A, -c B, a, b. I B = 90°—A,.a = 0;uig A, h = c cog A,
<br />Solution='of Oblique Triangles
<br />[31veu Required
<br />r j/ 3 �S`•% insin B a
<br />f r' I �'`B'a a' e, C b= sing �C=180°-(A+-R), sin C
<br />c=
<br />Iain A ;
<br />b sin A
<br />f C ."' 18Q —(� ."F Bl C a 61n Ci 4
<br />A; a, -b B, c, C einB ,i%— ° J =
<br />b, C =d, B, e a ° (a—b) g d B t
<br />:A'�-B=180 —G, tan B)� + ). 7y
<br />s?
<br />...,sin A'
<br />a, b, a A, Bi"o !A, b_ c
<br />Z.
<br />3� 'cinlB= YYY(,—a)(8—cj C= -i-
<br />180°—(AB)
<br />� •� a c ssr
<br />a+b+c
<br />µ 2.
<br />1C EvZ �'' n 'a• 3,' c. Ares e= - 2
<br />r
<br />A, b, -c Areaarea — 3a sin
<br />A "
<br />rt'
<br />�S oa O t3 Zlt r, 7J — a= win B sin C` r;
<br />A, B,C,a Area Brea =
<br />2 sin A. ;
<br />: REDUCTION TO HORIZONTAL
<br />oHorizon
<br />tal distance= Slope distance multiplied by the,
<br />S .= / 3 wee cosine of the.veoticalangle. Thus: slope distance=319.4 ft., "
<br />Vert. angle 5 10 1., From Table, Page 1X. cos 5° icy=
<br />r p , Q
<br />. }' � ' ', / i e'at lc '�' Horizontaidistance 319.4X.9959=318.09ft,
<br />510pg Horizontal distance also Slope distance minus slope
<br />A a distance times (1—cosine of vertical angle). With the
<br />! / ' - t 4e same figures as in the preceding example, the follow- ns
<br />3 0C, r { Horizontal distance Ing result is obtained,. Cosine 5°101=.9959.1—.9959=.0041:
<br />319.4X.0641-1.31. 319.4-1.31=318.09 ft
<br />Z�` r �J - < ' (,., _ t When the rise is known, the horizontal distance is approximately:—tbe slope dist-
<br />1ante less the square oft he rise divided by twice the slope distance. Thus: rise=l4 ft.
<br />'slope distance=302.81t. Horizontal distance=3028— 14 X 14 —30 ".32=��� -
<br />2X3112.13
<br />. _ -MAGE in U. 8. A.
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