|
Z-
<br />j G5�6
<br />TRIGONOMETRIC FORMUL)E
<br />o a c a c a
<br />A b �CA� b CA b
<br />•.R_ ight Triangle Oblique Triangles
<br />Solution of—Right_ Triangles•
<br />For Angle A. sin= a , cos = o , tan = . b , cot = - , sec = b , cosec = a
<br />Given Required
<br />72
<br />a, b- A,B,e tan A=.b=cot Ac= a2+ z=a 1 }
<br />a
<br />--. % a, cA, B, b sinA = a =cosB, b= /(0+q)(-) =c
<br />as
<br />02
<br />A, a P,` b, c B= 90°—A, b= a cotA, c= a
<br />sin A.
<br />A, b B, a, c B=90'—A, a b = b tan A, c = cos A.
<br />A e B, a, b B=90°—A,a=csin A,b=ccos A,'
<br />Solution -of Oblique Triangles
<br />Given Required ; .a sin B\
<br />b = , C 180°= a sin C
<br />A, B, a b, c, C . _ sin A (A-+ B)' -o —' sin A •
<br />— b sin`A a sin C
<br />A, a, .b B, c, C sin B = a , C = 180°—(A + B) , c = sin A
<br />a, b, O d, B, c A+B=180°— C. tan 1'(A—B)= (a—b) tan a (A +B)
<br />ab
<br />o=asin C
<br />+
<br />sin A
<br />b, o A, B, C s=a+2+c,sin�A=N(s b)(o—c
<br />sin aB= `f ac C 180°—(A+B)
<br />a, b, c Area s = a+2+c , area = s(s—a s—b (s—c
<br />A, b, c Area b o sin A
<br />area = Z
<br />as sin B sin C
<br />A, B, C, a Area area =
<br />2 -sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />S�aoce
<br />cosine of the vertical angle. Thus: slopedistance=319.4ft.
<br />, Vert. angle =50 101. From Table, Page IX. cos 50 10-
<br />e a M 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />c,1o4 A'C 1V 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 />Horizontal distance ing result is obtained. Cosine 51 10l=.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=302.6— 14 X 14 =302.6 0.32=302.28 ft.
<br />2 X302.6
<br />f
<br />Y. 8. Al
<br />
|