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TRIGONOMETRIC FQRMULfE
<br />4, d. 73 It B
<br />1; Right Triangle Oblique Triangles
<br />Solution -of Right TriangIes
<br />For Angle �, sin — e cop= •, tan = ,cot = ¢ ,sec = a , cosec =
<br />,,. ¢
<br />f j• Given Required 72¢
<br />n, b :1, B. ,c tan l = v —cotB, c — �/r r Ge = IZ I Qz
<br />a, c - _l, 'B, b sin A_ C = cos B, (11)
<br />d, a I3, 'b a 13 = 900—A b = a cotA, c = `�
<br />sill
<br />✓ ��[ f t q, b B, a, c B = 90'-21, a = b ren A, c = b
<br />f cos A.
<br />A, L',tc,h. B=9i1° :4,ct=csin.4,b=ccosi,
<br />Solution of Oblique Triangles
<br />Given Rc�luired +
<br />g, B, a b C, C b — lsinn 1 C —'-180'—(-A -i- B), c = sin rl
<br />1• t h sin _4 (& sin C
<br />-- A, a,. b' B, e, C sing= a C= I$0°—( -1 B}, c.= sin A
<br />b, G'. q, B;r, _4 �B-1Fd°— C, tan j (=t— B}= a—b) tan.-,' (A+B)
<br />_ a cin C a I h
<br />. sin A
<br />7
<br />¢, b, o A, B, 2tb r c
<br />� - - �' .9 = ` ,sin _2=, ir. _
<br />-
<br />sin,2B= ` ',B=C=180°---(_R-1-B)
<br />_ ac
<br />a, b; a Area=a2
<br />• _`
<br />A, b, c Area area = L e sin I
<br />a= sin B sin C
<br />1 i d, B, C,a Area arca 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 />1 + _ �s�°e Vert. angle —60 10. From 'fable, Page IX. ccs 50 101=
<br />` e otic h 0959. Horizontal distance=3124X-9959=318.09 ft.
<br />c�o4 �oI-,e Horizontal distance also=slope distance minus slope
<br />4e t. distance times (1—cosine of vertical angle). With the
<br />_ same figures as in the preceding example, the follow-
<br />1 Horizontal distance ing result is obtained. Cosine 50101-059. 1-91MO=X0,11.
<br />� _ � - � 319.4X.0041=1.w1. x19.4-1.31=318.03 ft.
<br />- * •- When the rise is known, the horizontal distance is approximately:--the slope dist-
<br />_ ince less the square of the rise divided by twice the slope distance. Thus: rise=l4lt.,
<br />Y � r slope distance=3026 ft. Horizontal distance-502.6— 14 X 14 =8020-0.32=302.2E ft
<br />2 X 302.6
<br />IL
<br />MARE IN p,8. A.
<br />%. °'�i
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