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I
<br />Zc
<br />;i
<br />30..
<br />TRIGONOMETRIC FORMULIE
<br />? A A:/ ,
<br />b C
<br />`Right Triangle Oblique Triangles
<br />Solution of Right. Triangles
<br />For Angle A, sin=a , cos= b , tan= a ,cot -- .b , sec. ,`cosec =
<br />c c b a b a
<br />Given - Required
<br />a, b A, B4O tan A = b = cot B, c = o + z =' a
<br />a, c A, B, b sin = c=cosB,b=,�/(c+a)(c—a)
<br />A, a B;'b;-cB=90°—A, b = acotA,c= a
<br />4. sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />A, c. B, a, b B=90°—A, a = csin A, b=,.c cos
<br />Solution of Oblique Triangles
<br />I
<br />Given
<br />Required
<br />a sin B a sin C
<br />A, B, i
<br />b, q 'C'--.
<br />b _
<br />' = 180°—(A +'B), c —
<br />sin A sin A
<br />A, a, b
<br />_t.1
<br />=B, c, C
<br />sin A a sin C
<br />sin B = , C = 180°—(A + B) , c =
<br />a sin A
<br />a, b, C_
<br />A, B,. c
<br />A+B=180°— C, tan ; (A—B)= (a—b) tan J (A +B)
<br />a + b
<br />a. sin C
<br />sin A
<br />s
<br />a, b, c
<br />A, B, C`
<br />s=a+2+c,"."I V
<br />be
<br />sin;B=`I(3—aac ),C=180°—(A+B)
<br />a, b, c
<br />Area
<br />s=a+b+c (— ) ( c
<br />2 ,area = s a a s— s —
<br />A, b, c
<br />Area
<br />area = be sic A
<br />2
<br />aQ sin B sin, C
<br />A, B, C, a
<br />Area
<br />area =
<br />2 sin A
<br />REDUCTION
<br />TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />e
<br />cosine of the vertical angle. Thus: slope distance=319.4ft.
<br />a�5�o�e
<br />Vert. angle= 50 10'. From Table, Page IX. cos 50 10/=
<br />e
<br />SX
<br />9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />Horizontal distance also=Slone distance minus slope
<br />Ao¢�e
<br />-4 .
<br />a distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance
<br />ing result is obtained. Cosine 51 101=.9959.1—.9959=.0041.
<br />When the rise is known,
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />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.
<br />Horizontal distance=302.6— 14 X 14 =3026-0.32=30228 ft.
<br />2 X 3026
<br />MADE IN U. 8. A.
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