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I
<br />TRIGONOMETRIC FORMULlE=
<br />i
<br />�f B B B
<br />a ° a c a
<br />-r- g b CAC
<br />.b C A b
<br />h _ Right Triangle Oblique Triangles —J
<br />Solution of Right Triangles
<br />-1
<br />I >
<br />For'Angle A, sine= a , cos = b ,tan = , cot = b , sec = o , cosec = e
<br />- c c b a b a
<br />Given Required 2
<br />4 a, b ' A, B ,c tan A = b = cot B, c = a2 + 2 = a 1 + az '
<br />2
<br />a, c -A, B, b sin A = c = cos B, b= \/ (c+a) (c—a) c 1= u
<br />z' A, a B, b, a B=90°—A, b= a cotA, c= a
<br />sin A. -
<br />A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />A, e B, a, b B = 90°—A, a = e sin A, b = c cos A, '
<br />k Solution of Oblique Triangles
<br />Glven Requireda sin B' ° a sin C
<br />} i A, B,.a ' b, c, C b = sin A , C = 180 —(A + B), c = sin A
<br />b sin A
<br />A, a, b B, c, C sin B = , C = 180°—(A (B), c a sin C
<br />a = sin A.; .
<br />a, b, C A, B, c A+B=180°— C, tan ; (A-B)= (a—b) tan % (A +B)
<br />a'+ b
<br />c=
<br />a sin C
<br />sin A
<br />aa+b -+c
<br />Ja, b, o A, B, C 8=2 in J,A= b e
<br />sin ZB='I(s—a)(s—c ,C=180°—(A+B)
<br />Y ac
<br />a+b+e
<br />a, b, • o - Area S = 2 , area = s(s—a s—) (s—c
<br />A, b, c Area area = b c sin A
<br />2
<br />a2 sin B sin C
<br />- -_ A,B, C,a `Area' area = 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 />` I t9rce Vert. angle =5° 10�. From Table, Page IX. cos b° 101=
<br />e a1 y9959. Horizontal distance=319.4X.9959=318.09 ft
<br />Slop Aw$1e a Horizontal distance also=Slope distance minus slope
<br />4e distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />Horizontal distance ing result is obtained. Cosine 50 101=.9959.1—.9959=.0041.
<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 />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X 14 =302.60.32=30128 ft.
<br />2 X 302.6
<br />MADE IN U. 8-&
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