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TRIGONOMETRIC FORMULjE
<br />L:J11 ?10
<br />b C .Ab C A C
<br />�:✓•) `� , Right Triangle Oblique Triangles
<br />2,4,, �. = - ✓ �, Solution of Right Triangles
<br />?' - �- ----`- a b a b c c
<br />J� %
<br />IFor Angle A. sin = c ,cos = c -,tan= L cot- ¢ -,see= b , cosec = w
<br />�, o !O �S L� o .i Given.'" rRenuired
<br />L a, b. - A, B ,c tan A = = = cot B, c = -777 z =.a 1 +
<br />3 G C fi� Z Sw- f b a2
<br />v
<br />7 a, c 1, B; b .o a.
<br />L ,,
<br />.r
<br />.;" t <• 6 -' =;7 A, a B, b, c -B-90° A, b - a cot A, c= a iW
<br />sin A.
<br />lt j A, b - B, a, .c B= 90°—A; k = b tan A, c = cos A. ,
<br />A, c . B, a, b B = 90°—A, a = a sin A, b - c cos A,
<br />Solution of Oblique Triangles
<br />r r Given Required
<br />ivo • , i.% 1? t; A, B, a b, c, C. b = sinnAB > a = 180'-(A + B), c -7 sin A
<br />b sin A a sin C
<br />A, a, b B, c, C sin B= , C = 180°-(A ( B), c
<br />z".4a'O ��•� "a- sin �-
<br />_1�_[l b, C A B,c A ° ic-b)tanz(A}B) w
<br />+B=180 - C, tan zt `(
<br />L �t 7 ( ✓ . �--f. `fi 'y5�- _ - a sin C ¢ +
<br />sin A
<br />¢ b c din �A, B, C s,=a+b+c r _-
<br />,. 2 ,sb c a
<br />"y' dr-. 3y. 5 ✓_ (
<br />f� sin-i-
<br />zB_,,f ,a=Iso°-(AB) �=
<br />7- (,,may f; }� d f -V
<br />�a+b+c
<br />a, b, c Area s= 2 ,area = s(s-a s— s—c)
<br />.�- � r r ,� . , • ° � g, b, c Area area =
<br />f
<br />i Z Z. os az'sin B sin C
<br />.L? b �, B, C, a Area area -
<br />G 2 sin A
<br />=-r—REDUCTION TO HORIZONTAL
<br />j C_� _ �•�i . _ �''? ,
<br />09 ' %(' Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distanceVert. anle= 50 M From Table, Pa=319.4ft. G
<br />IY- cos
<br />-P g = � a y 9959:• Horizontal distance=319.4X.9959 318.09 ft.6° la
<br />(�:r' `^tft7'._. 5104 �g>e a Horizontal distance also =Slope distance minus slope
<br />distance times (1-cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />ing
<br />ollow-
<br />d� Horizontal distance ingresuIt is obtained. Cosine 50101=.9959.1-.9959=.0041.
<br />�1M Lj ' p , ?1 /� 319.4X.0041=1.31.319.4-1.31=313.09ft.
<br />` � +� �� 0 �r l When the rise is known, the horizontal distance is approximately:-the slope ist-
<br />.r r b Y� r z anee less the square of the rise divided b twice the slope distance. Thus: rise=l ft,
<br />slope distance=502.0 ft. Horizontal distance=302.0- 14 X 74 =�0� 32_2fL
<br />2 X 302 e,
<br />,r r _ _ - • . a - w • w � , .. .. E.t '�`. MAGE 7N 0, g, A,'..
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