|
,Z TRIGONOMETRIC FORMULIE
<br />- �✓ Sv t tlr �� B B
<br />7f C �b C b � � _,'.��:.•� ����: �� ;;q,;' '� Right Triangle Oblique Triangles
<br />J- . ^ Solution of Right Triangles
<br />_ a b a. b b c
<br />For Angle A,sin = e , cos = c , tan= .b cot = a , sec = b , cosec =
<br />a
<br />c2- Given Required
<br />b1z
<br />tanA=a a +a,A,B,c ,
<br />.a
<br />A, B, b sin A. a Cos B, b= c a c=a aas
<br />A, a B, b, c 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 =
<br />cos A.
<br />�> A, c B, a, b B=90'--4, a = c sin A, b= c cos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />/ ' a sin B' - asin C—
<br />r �?
<br />A, B; a b> c, G' b = sin A ' C = 180°—(A } B), c = sin A
<br />in C
<br />A, a, b B, c, C - sin.B = b sin A,C = 180°—(A + B), c = sln A
<br />L 4�ti t 4 a, b, C A, B, c A+B-180°— C, tan J (A—B)= b
<br />(alb) tan 2 { B)�
<br />—.a sin C a + b
<br />J
<br />t sin A
<br />a+b F e �(s—
<br />a, b, c A, B,.0 's= 2 in 2-A1= be
<br />N.
<br />7 sin 'B= J(4—aa c
<br />a,a+b+ c
<br />N a, b, c Area s = 2 , area = V. (s—a) (s--) (s—c
<br />IN flI I t •,
<br />��� i� ` I t`c �.1. d;'b; �c Area area = b e s A
<br />as sin B sin C
<br />,�;B, C,a Area. area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />-- �� Horizontal distance= Slope distance multiplied by the
<br />I ` cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />Vert. angle =51 101. From Table, Page IX. cos 601(Y=
<br />- r e ass y 9959. .Horizontal distance=319.4X.9959=318.09 ft.
<br />ca�op An�Ne a horizontal distance also=Slope distance minus slope
<br />nn distance times 11—cosine of vertical angle). With the
<br />Qe same figures as in the preceding example, the follow-
<br />` Horizontal distance ing result is obtained. Cosine 50101=.9959.1 .9959=.0041.
<br />i
<br />319.4X.0041=1,31.319.4-:-1.31=318.09 ft.
<br />I When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />•' r - ante less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=302.6 ft. Horizontal distance=3026-2 3026=302 6-0.32=302.28 ft
<br />9
<br />MADE IN U. 6. A.
<br />
|