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I TRIGONOMETRIC FORMULfE
<br />��.27J 9 a a c a c
<br />- _ b. C 1,b C b
<br />/°� .�,._:� •r ti �,i _. p Right Triangle I Oblique Triangles
<br />��, x� �:l.�"�i o �- �� Solution of Right Triangles
<br />For Angle A. sin= c , cos = , tan = b „cot = Q , sec = b , cosec =
<br />Given } 'Required 2 a
<br />tan A = b =cot B, c = 2- = a 1 + s
<br />.
<br />a
<br />a, c A, B, b sin A = c = cos B, b = \1(o+a) (c—a) = c 1 — 02
<br />- 7J7 A,a B, b, c B=90°—A,b=acotA,o= a
<br />✓ sin A.
<br />-4, A,b B, a, c B=90°—A,a=btsnA,c= b
<br />y ) 8. cos A..
<br />A, c B, a, b I B= 90°—A, a= c sin A, b= c cos A,
<br />j 'G a bS Solution of Oblique Triangles
<br />j _ S V r p- Given Required a sin B _ a sin C
<br />i a � f IZr 7 � . � �1 A, B a b, e, C b = sin A ' C — 1`0�—(A + B) , c =
<br />sin A
<br />et r- b sin A a8 ill C
<br />A, a, b B, c, C sin B= a ,C = 180°—(A fi B), c = sin A
<br />—... a—Fi) tan '_(-� +B)
<br />•r .x• y�$ ri. j a b, C A, B, c A+B=180°—C, ten (A—B)= ,
<br />a + b
<br />a sin C
<br />sin 11 -
<br />fd , a+b +c il,
<br />�," i` t• y. 1 a,, b, c A, B, C s= 2 sin A= \ b c '
<br />sin 1B— C=180—(.A.+B)
<br />r _ a, b, c Area += 2 ,arca
<br />1
<br />��-•�� 1` b c sin A
<br />II r„ ti A, b, c Area area
<br />a'- sin B sin C
<br />_ _ J A, B, C, a Area area = 2 sin d
<br />e
<br />`l REDUCTION TO HORIZONTAL
<br />t r Horizontal distance=Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope dist an ce =319.4 ft.
<br />i _ " t4oce Vert. angle=5° b0'. From Table. Page IX. cos 5'101=
<br />1 ' e a 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />{ ' { ° - glut' ogle x Horizontal distance also=Slope distance minus slope
<br />e t. A 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 6'10'=.9959. 1—.J959=.0041.
<br />t, 319.4X.00+1=1.31.319._ 131=31&09 ft.
<br />When the rise is known, the horizofital 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 />( rj • r i slope distance=302.6 ft. Horizontal distance=30'2.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />C
<br />1 / 2 X 302.6
<br />- ^- MADE IN U. 6.A,-, •
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