Laserfiche WebLink
TRIGONOMETRIC FORMULAE <br /> '71 X4`3 a B B B <br /> 3.0/ <br /> a a o a <br /> _ ._.�_.. <br /> j <br /> 3 f V C Al, b C A b C <br /> Right Triangle I�Oblique Triangles <br /> Solution of Right Triangles <br /> -3 . <br /> ` 0,P For Angle A. Bin =a,cos= b,tan= a,cot =b,sec=°, = a <br /> -3 3, / rs 3 c a b a cosec b a <br /> 9 -- Given Required a s <br /> ° ` a b A B,a tan A= b= cot B,c = as+ s =a 1 <br /> b +T2 <br /> 9 3 S 3 3 i % a, c "8. b sin A=a cos B,b= -a(a+a (c =c 1 a3' <br /> G <br /> A a 40 B=90°-A,b =acotA,o= a <br /> sin A. <br /> 3 9 ,1h• +1 a B=90°—A,a = b tan-A,c= b <br /> Z 7 I _--.__'", T cos A. <br /> 4 7 a i ay b, 1 B=90°—A,a=a sin A,b=o cos A, <br /> 'Solution of Oblique Triangles. <br /> -- <br /> Given Foquinad <br /> asinB <br /> 3 S - B.a b. rs, O b= , C= 180°—(A+B), o = sin A <br /> ein A <br /> 5. 7 b sin A <br /> 2 <br /> ay-C a sin B= .C= 180°-(A+B) a = a Bin C <br /> L9 r ,.. _ Bin A <br /> A{ 8=180°-C,tan;(A-B)= a-b)tan�(A+�1 <br /> 3 J %6 a+ b--�71 <br /> _ a sin C <br /> L` c sin <br /> 8=a+2 ,ein.+}A= <br /> r o <br /> sin g__�(s—axs—o <br /> ac ,C=180°--(A+B) <br /> a, b, c Area a— 2 , area = a a—a s-- s--o) <br /> J / b c sin A <br /> A, b, c Area area = <br /> 2 <br /> S as sin B sin C <br /> _ A,B,C,a Area area = <br /> 2 sin A V ` 1 REDUCTION TO HORIZONTAL <br /> Horizontal distance—Slope distance multiplied by the <br /> cosine of the vertical angle.Thus:slope distance=119.4 tL <br /> a-Is�sooe s VerL angle=6°Id. From Table,Page IX,cos 6°10y= <br /> 996& Horizontal distanoe=819.4X.9969=91&09 ft. <br /> S" } S%off Ara1e Horizontal distance also=Slope distance minus slope <br /> 94 <br /> 1 C' .t Qe 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 60 10P=.9969.1—.9969=.0041. <br /> J`✓ When the rise is known,the borixonlal dis ance is approximately:—the slope dist- <br /> ance less the square of the rise divided br twist the slope distance. Thus:rise=14 fL, <br /> slope distance=502.61L Horizontal distanf—=6—14 X 14-4MO—M32=302.28 fL <br /> 2X=16 <br /> A <br /> .1 <br /> . 014 M U.4.A. <br /> F ' , <br />