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<br />_ �-!"'• r'S ( �C i. ? G�TRIGONOMETRIC FORMULfE 7_
<br />�� Z 70 �C�2.�s',. bt- r X2•.7 B ;
<br />B
<br />'Z-
<br />.3 :r_-4- m.4- c t""c a a o a
<br />-z
<br />r_.... C
<br />�g0Z - A b C ��6 C
<br />Right Triangle Oblique Triangles
<br />:�ga �; ��%� 3 Solution of Right Triangles
<br />sin a, b a b c c
<br />For Angle A, = cos= c , tan= T, cot = a , sec = b, cosec = a
<br />�� jvii 0 Given Required 2 a
<br />/ vliY p p -r-= �p f; a, b, A,B,c' tanA=b=cotB,c= as } s=a 1 I a
<br />a- - - las
<br />_ -! �' �' \Q•2$ a, o A; B, b' -.sinA --� -cos B,b-�(c+a)(c a)=c�l-oa
<br />, d, a -B, b, c . B=90°=A, b = a GotA, c= sin A.
<br />A, b. B, a, c :B = 90* -A, a = b tan. A, c = b
<br />cos A.
<br />Q
<br />` ✓ °° ' b 0' J % _`[, 1 P• A, c' B, a, b ' B = 90°-A, a = c sinA, b = c cos A,
<br />Solution of Oblique Triangles
<br />170---J 0 Given Required
<br />{0 11 t4 A B,a b c,,C b=asin B C=180°-(A+B),c=asin C
<br />_j sin ' . sin A
<br />cp
<br />o- - 1 G'so b iin A ° a sin C
<br />o S -a . /rS' A, a,' b B, c, C sin B= d ,C = 180 -(A (B), c - sin A
<br />Ga, b, C d, B, c A+B=1800- C, tan z (A -B)= (a -b) tan s (A +B)
<br />F6 a sin C S"
<br />sin A
<br />Tg al b -z 4, c A; B, C s=a F 2+c,sin;A= V(s- b)(c-c
<br />'�\\ C`�Jy� sinaB=�Y(s-aa(� c ,C=180°-{A+B)
<br />i, a�b�c
<br />(s -a s- (s-
<br />�j��
<br />ZS' c Area s= 2 , area = sc
<br />6 h
<br />A, b, c Area area =basin
<br />�Z S es -,5; 5-0 as sin B sin C y, 10 i
<br />�S A, B, C, a Area area '_
<br />2 sin A.
<br />T, -S f S'� , 9 C> Z - REDUCTION TO HORIZONTAL
<br />¢ O Z I Horizontal distance=Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />Staoce Vert. angle=51101. From Table, Page IX. cos 5'101=
<br />9959. Horizontal distance=319.4X•9959=318.09 ft.
<br />e cope �distance ttimest(lcco ine oflvertcal angle). With slope
<br />W ththe
<br />same figures as in the preceding example, the follow -
<br />S -7 % C G
<br />r Horizontal distance ing result is obtained. Cosine 50 10f=.9959.1—.9959=.0041.
<br />j
<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 />0 O ante less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />v Z - slope distance=302.6 ft: Horizontal distance=302.6— 14 X 14 =302 —0 ft.
<br />— 2 X 302.6
<br />SI O MADE IN U. a. A.
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