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L
<br />g,Z24- 0 0
<br />7, 7-
<br />j
<br />TRIGONOMETRIC FORMUL&
<br />B
<br />B
<br />ac a a
<br />b b C C,
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle'14. Sin = a , cos tan= a T , cot = b , sec cosec
<br />' ' 0 a 7
<br />Given Required ¢
<br />a, b A, B,c
<br />tan A =a cot B, o = V a2+ 2 a+ 7a-
<br />4, o. A, B, b sin = 7—a2
<br />irt: I a
<br />A, a B, b, r B=90°—A, b = a cotA, 0=
<br />sin A.
<br />3. b
<br />A, b B, a, C B=90'—A, a = b tan A, c = —
<br />c.. A.
<br />A, c B, a, b. B=90'—A, a = esinA, b= ecosA,
<br />Given': Required Solution - of. Oblique Triangles
<br />asin B
<br />C , C = 180'—(A + B),
<br />A, B, a b, c, b
<br />3. sin A sin A
<br />a sin C
<br />1_7 A, a, b B, c, C sin B 0'= 180*—(A + B), c = sin A
<br />—C,tan (a—b) tan 11 (A+B)
<br />C A, B, 0 A+B= 180' n I (A�B)= + b
<br />a sin C
<br />Sin -A
<br />a+b+
<br />a, b, a A, B, C 8= 'sin 21A=
<br />2 N b c
<br />sin B— C 800--(A+B)
<br />-\ —ac
<br />b —_ (--
<br />a, b, a Area S=a+2+c N/T(,—aT .,— Y)
<br />in A
<br />A, b, c Areab*c s
<br />*
<br />2
<br />a2 sin B sin C
<br />A,B,Ca 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 />or �
<br />Vert.
<br />'co Ve aqngle = 50 101. From Table, Page JX. cos 50 101=
<br />661's1% 0) .9959. Horizontal distance�319AX.9959=318.09 ft.
<br />e IS , —
<br />K glop
<br />4 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 50 101=.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=302.6ft. Horizontal distance --.302.6— 14 X 14 =302.6-0.32=302.28&
<br />2 X 30.6
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