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,C/
<br />TRIGONOMETRIC FORMUL-4,1
<br />.. 11 1 a
<br />B B B
<br />-a a C a
<br />'A —A A_C
<br />6 b C 6
<br />kigb t Triangle T Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle
<br />+b
<br />A. sin
<br />a b a bb cot sec cosec
<br />ff Given
<br />'b
<br />Required
<br />A, B,c
<br />a
<br />tan = b = cot B, c =Va2-I- 2 2
<br />_+ 7
<br />,a2
<br />''
<br />B, b
<br />sin A cos B, b %/-(c +a) _(o a) o all
<br />1.
<br />02
<br />A.b; e
<br />B=90'—A, It = a cotA, c = a
<br />sin A.
<br />A, b
<br />B, 4, 4
<br />B =90'—A, a = b tan A, c
<br />�os A.
<br />A, e
<br />B,, a, b
<br />I B = 90'—A, a = c sin A, It = o cos A,
<br />Solution
<br />of Oblique 'triangles
<br />Given
<br />A, B, a
<br />Required
<br />b, e, C
<br />b = a sin B asin C
<br />, C = 180--(A + B), c =
<br />sin A sin A
<br />A, a, b
<br />B, f,,
<br />b sin A a sin C
<br />sin B= C = 180*—(A + B), e =
<br />,. -C
<br />a sin A
<br />a, b, C
<br />*A, B, c
<br />�'�
<br />A+B= 180'— C, tan (A—B) = (a—b) tan (A+B)
<br />'b
<br />+ I
<br />a sin C
<br />sin A
<br />a, b, a
<br />A, B, C
<br />a+b+c
<br />S = — Is 'in �A=�
<br />2 b
<br />r
<br />sin'B= C=1800--(A+B)
<br />2 1
<br />a e,
<br />'
<br />a, b,''c Area 8=a 2-T-
<br />, area — 11s(s—a)
<br />cvp A, b,6 Area are. b e sin A
<br />2
<br />a2 sin B sin C
<br />\`11� { A, B, C, a' Area area
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />e �Acosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />Vert. angle= 51 101. From Table, Page M cos 51 IW=
<br />.9959. Horizontal distance�319AX.9959=318.09 ft.
<br />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 10I=.9959.I9959=.004I.
<br />319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br />When the rise is known, the orizontal 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 X 302.6
<br />KADE M U. B. 06
<br />F
<br />E
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