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<br /> /iC 1Yaexf WP
<br /> TONOMETRIC FORMUUE
<br /> r'EFvulR;
<br /> B
<br /> To pumr tdk;cA)j B
<br /> Gtluin/ Q6GtIc+trF GTdL a d
<br /> a
<br /> Ooo3, - ,* b � A b � C
<br /> ' �., Oblique Triangles
<br /> D 06 33 3 — of Right Triangles
<br /> S m b a b o 0
<br /> r S Por _
<br /> Anile x ,6os ,tan= ,cot = a,see=b, cosec=
<br /> D O IO ?n„ _ (uvea tt o b a
<br /> a, b B,a N tan.Al=b= cot B,a = a2 I =a1�+��s
<br /> cv s Y W
<br /> m @ o * . 0. 0 A A b sin A=a =cos B,b=%1o+a c—a •=o
<br /> 30 A,a B, b, o B=90°—A,b=a cotA,o= a
<br /> 7-r' Y .3 9t sin A.
<br /> b f
<br /> d,b B,a, a B=90°—A,a = b tan A,cc cos A. r
<br /> 4B=900—A, .r o
<br /> o B.a, b a=o sia A,b=a cos A.,
<br /> b� Solution of Oblique Triangles
<br /> c. . •sr L c'' a b C b =a sin B Lr= 180°—A B a sin C
<br /> sin A ' ( -) ). o =
<br /> sin A
<br /> b sin A
<br /> �rl3 3a d, a, b
<br /> B,a, sinB= ,C= 180°—(A-i-•B),a = snA
<br /> i .•/ ,' a
<br /> A,B,o A+B-180°—C,tan'v(A—B)= —b)tank a (A+B)
<br /> a+ b
<br /> _sem , �-�o o — aeina
<br /> sin A
<br /> X 9
<br /> -- --- �.�{l fn/° Iv•F°t” ., sin;B=�x—a}(a-a �C=180°—(A+B)
<br /> ac
<br /> a+b+c
<br /> .4% Area 8= 2 ,area =,v/a a—a s— s
<br /> A, b, a Area area = b c i A
<br /> _ 1—42 ?9 ,3 8 as sin B sin C
<br /> a 2 t•�y 3 9
<br /> 5 A,B,C, Area area = 4
<br /> 5 2 sin A 3
<br /> REDUCTION TO HORIZONTAL
<br /> ' Horizontal distance—Slope distance multiplied by the
<br /> q(, 7 + cosine of the v cal
<br /> N«� ce grtf atyfiom.Thus:slope diataa�X919.4 ft.
<br /> 7 4 p 9� Vert. Horizon5ttal d-64toe�S UX.9f S&oofftb°IW-
<br /> 9M.
<br /> �a� `� aMO1e Horizontal distance also=Slope distance minus slope
<br /> z 6` v ,same figures as i to henereofedVertical angle). With the
<br /> D ng example,the follow-
<br /> 7 s er distaueo ing result is obtained.Cosine b°10'=.9M&1—.8869=.0041.
<br /> / — a
<br /> when rise is known. 819.4X.0041=1.31.919.4-1.31=91&09 ft.
<br /> own,the horizontal distap"ce is approximately:—the slope did-
<br /> '3 ante less fhb sQuare of the rise divided by twiosthe slope distance. Thus:rise-14 it,
<br /> slope distance=892.8 ft• Horizontal distance=3me—14^ 14 Boz e-o rtaaoaze
<br /> a e ;
<br /> •
<br /> or
<br /> OK
<br /> r
<br /> I •
<br /> it -/ . • ..
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