|
7—f
<br />C11 .4-
<br />/60
<br />TRIGONOMETRIC FORMULS
<br />B
<br />B
<br />-e
<br />a a a
<br />A A
<br />C 0
<br />Right Triangle-
<br />Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin
<br />�cos = b tan a b cot = , see cosec
<br />Given
<br />a. b
<br />Required72-
<br />A, B,c
<br />a
<br />tan = cot B, c +-72- =aVI + 32
<br />4,
<br />A, B, b
<br />a2
<br />sin A = cos A b V (c+a) (o--a)c 1-73
<br />A, a
<br />B, b, I;
<br />B=90°—A, b = a cot A, c= a
<br />sin A.
<br />A, b
<br />B, a, e
<br />B=900—A,a = btan A,c= b
<br />cos A.
<br />A, I;
<br />B, a, b
<br />B=90*—A, a = o sin A, b = c cos A
<br />Solution of Oblique Triangles
<br />Given
<br />A, B,.a
<br />Required
<br />b, c, C
<br />asin Basin C
<br />b = , C = 180--(A + B), c =
<br />sin A sin A
<br />A, a, b
<br />B, c, C
<br />b sin A asin C
<br />sin BC = 1801—(A + B),
<br />a sin A
<br />h, C
<br />A, B, c
<br />a—b) tan,-�' (A+B)
<br />A+B=180°— C, tan 'i (A—B)=
<br />a + b
<br />a sin C
<br />sin A
<br />+b I
<br />a, b, a
<br />A, B, C
<br />S =a 2+ .8injA= N
<br />b
<br />sinjB= ('qa)—()'C=180-4A+B)
<br />ad
<br />/A
<br />a+b+c
<br />a, b, o
<br />Area
<br />s= — , area
<br />2 . VS(T—T(S-3T01—
<br />A, b, I;
<br />Area
<br />besinA
<br />area =
<br />a2 sin B sin C
<br />A,B,C,a
<br />Area
<br />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 />Vert. angle,=50From Table, Page IX. cos 51 I(Y=
<br />"ovegee
<br />v .9959. Horizontal distance=319AX.9259=318.00 ft.
<br />-4 Horizontal distance also=Slope distance minus slope
<br />distance With
<br />times (,_cosine of vertical angle). the
<br />Horizontal distance
<br />same figures as in the preceding example, the follow -
<br />-.g result is obtained. Cosine 5Q l0,=.9959.1—.959=.0041..
<br />319.4X.0041=1.31. 319.4-1.31 =318.09 ft.
<br />When the rise is known, thehorizontaldistance is approximately:—the slope dist-
<br />anee less the square of the
<br />rise divided by twice the slope distance. Thus: rise=14fL.
<br />slope distance=302.6 ft.
<br />Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />MADE IN U. S. A.
<br />
|