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TRIGONOMETRIC FORMULAE
<br />' B B B
<br />e a c a c a
<br />cC
<br />b A b aA b C
<br />s' C
<br />:7 Right Triangle Oblique Triangles
<br />C7 ✓ ". �Solution of Right Triangles a b a b c a
<br />I, For Angle A. sin = c , cos = a , tan = b , cot= a , sec = h , cosec = a
<br />+� Given Required
<br />b.- A, B ,c tan A = b =cot B, c = az + a,=
<br />9
<br />A, B, b sin A = = cos B, b = (c -f a) (a—a = e Vi a
<br />A' a B, b, c B=90°—A, b= a cotA, c=
<br />sin A.
<br />,I S
<br />A, b B, a, e B = 90°—A, a = b tan A, e=
<br />/ cos A.
<br />J A, c B, a, b I B = 90°—A, a = e sin A, b = e cos A,
<br />_ Solution of Oblique Triangles
<br />/ Given Required
<br />(� A, B, a b, c, C b = sin A ' C = 1801—(A + B), e = sin A
<br />l d r b sin A, a ein C
<br />A,a,b B,c,C sinB= a ,C=180—(A+B),c= sin
<br />0
<br />b, C A, B, c A+B=180°— C, tan j (A—B)= (a—b) tan j (A+B)�
<br />a b
<br />i a sin C +
<br />sin A
<br />a, b, a A, B, Cs=a+2+a,sin A=N be
<br />[ 3 a 8—a
<br />ein71B=. Ja c�,C=180°—(A-}-B)
<br />�J of a+b{c
<br />a, b, e Area 8= 2 area= s(8—a s— (s—e
<br />(! bcsic A
<br />A, b, c Area area = 2-
<br />a' 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 />�sope Vert. angle=51 101. From Table, Page IX. cos 50 10•=
<br />ass 9959. Horizontal distance -319.4X.9959=318.09 ft.
<br />r S,,,De Arge Horizontal
<br />distance lee distance 1tlthedistn es(lcosine of vertical angle). With
<br />— Ve same figures as in the preceding example, the follow -
<br />Horizontal distance
<br />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=3026 ft. Horizontal distance=3026— 14 X 14 =3026-0 32=30228 Yt
<br />2 X 3026
<br />4 MADE IN U. I. A.
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