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TRIGONOMETRIC FORMOL&
<br />33 B B
<br />a
<br />a E a c a
<br />A— � A G
<br />Right Triangle Oblique Triangles
<br />Solution.
<br />For Angle A. Bin = , coo= b , tan= a , cot = b , sec = q, cosec = °
<br />b b
<br />Given
<br />a,b
<br />Required
<br />A,B,a
<br />c c a a
<br />tan A=b= cot B,c= aQ } ==a 1+
<br />aR
<br />q e
<br />A, B. b
<br />z
<br />sin A = = cos B, b = �/ e -E -a) (E—a = c 1—a
<br />A, a
<br />B, b, a
<br />B=900—A, b= acotA, c— a
<br />Bin A.
<br />A, b
<br />B, a, e
<br />B = 90°—A, a = b ten A, e = b
<br />C68 A.
<br />A, E
<br />B, a, b
<br />B = 90°—A, a = e, sin A, b = a coo A,
<br />Solution of Oblique Triangles
<br />Given
<br />A, B, a
<br />Required
<br />b, G,
<br />b _ a sin B , C 180°—(A + B), ° —
<br />_
<br />Bin A'
<br />BIII A 61n A
<br />A, a, b
<br />B, E, iii
<br />b sin A a sin C
<br />BIn B= ,t�i = 180�'—(A -I- B), G =
<br />I
<br />a Bin A
<br />a, b, C
<br />A, B, E
<br />A+B=180°-- C, tan }(A—B)—{a— b) tan � B)
<br />6
<br />a -}- b '
<br />a sin Cr
<br />c=
<br />sin A
<br />g b, a
<br />A, B, C
<br />s—a+b+O,ein jA—
<br />.t
<br />sin#B� J a
<br />ac
<br />a+Z +d
<br />a, b, G
<br />Area
<br />a , area = 8(&—a s— o—c
<br />A, b, c
<br />Area
<br />area = b d sin A
<br />2
<br />a2 Bin B sin C
<br />A, B, C, a
<br />Area
<br />area = 2 sin A
<br />REDUCTION
<br />TO HORIZONTAL
<br />Horizontal distance=Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =318.4 ft.
<br />V9959.rt. e�60 101. IX. cos 6° Sd
<br />�5�4ce
<br />q Horizontal distance= 19.4X.8959= 3 8.09 ft -
<br />opc
<br />Sl A�1e
<br />C Horizontal distance also=Slope distance minus slope
<br />�e
<br />distance times (1 --cosine of vertical angle). With the
<br />Horizontal distance
<br />same figures as in the preceding example, the follow -
<br />ing result is obtained. Cosine 5° 10'=.9959.1—.9959=.[1041.
<br />319.4X.0041-1.31. 519.4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distanceis approximately:—the slopedist-
<br />ance Less the square of the rise divided by twice the slope distance. Tbus: rise=l4 ft.,
<br />slope distance=3028 tt.
<br />Horizontal distance=sms— 14 C 14 =�d8-0.32=302 28 Pt.
<br />2 X 302.8
<br />MADE IX V.6.4,
<br />of Right Triangles '
<br />
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