|
TRIGONOMETRIC FORM r
<br /> -- B 3C , Qo B 3 y . L B
<br /> 3 ¢ � 4
<br /> 6 f 3 Y. 4 / A c a �3 J' a 3 a
<br /> A
<br /> 3 G r b C A�b C b C
<br /> --�_ Right Triangle Oblique Triangles----1
<br /> 7 Solution of Right Triangles
<br /> ti" b I L,u V. For Angle A. sin=a
<br /> >' Given R C cosOS=b C,tan=ba,COt=b a,SeC=bc,Co6ec a—
<br /> u Required a
<br /> -, 37 a,b A.B,ctanA=b= cot B,c= a=+br=a 1+b
<br /> s at
<br /> a,c A,B,b sinA=a=cosB,b=V(c+a)c—a)=c 1—
<br /> -- c
<br /> ` p A,a B,b,c B—90e—A,b=a cot A,c= a
<br /> sin A.
<br /> A,b B,a,c B—90e—A,a=b tan A,c= b i/ --
<br /> cos A."
<br /> j ---/, p ® A,c B,a,b B=90°—A,a=c sin A,b—c cos A.
<br /> Solution of Oblique Triangles ,
<br /> Given Required
<br /> a stn B
<br /> A,B,a b,c, C b= sin,q ,C=180*—(A+B),c=a sin C
<br /> sin A
<br /> 1 3 ti ' d A,ab
<br /> a B,c,C sin B=b sin A
<br /> , C=180 —
<br /> (A+B),c=a sinC
<br /> 4 1 sin A
<br /> a,b.C A,B,c A+B=180°-C,tan}(A—B)_(a-b)tang(A+B)
<br /> c=asin C a+b
<br /> sin A
<br /> f # a+b+c a,b,c A,B,C s=
<br /> ' .sinA= b—Z
<br /> C" �/ 3 sin#B= (s—a)(s—c) C=180°
<br /> ac —(A+�
<br /> a,b,c Area s=a+b+c,area= s(s—a) (s—b) (s—c
<br /> S i' y A,b,c Area area= b e sin A I el ` 0r
<br /> A.B,C,a Area area=at sin
<br /> B�C2 sin
<br /> ' REDUCTION TO HORIZONTAL_
<br /> Horizontal distance-dope distance multiplied by the
<br /> cosine of the vertical angle.Thus,for a dope distance of
<br /> _ _ l 403.6 ft.and a vertical angle of V 4(V—the cosine of
<br /> 3 J �) V 4� from a table of natural trigonometrical 5 s�Angle. a
<br /> y v 9967,and horizontal distance-403.6:.9967
<br /> --- ---�- - -402.27 ft.
<br /> Horizontal distance also�S Horizontal distance
<br /> (� Tope distance mimus dope dis•
<br /> Cos-414W—.9967.1—.9967-.0033.403.6z.0033-1.33t (I—cosine of vertical angle).Using the same figures as in the preceo`
<br /> ft Horizontal • 6- f.\.. —
<br /> t 0 > When the rise u known, d!;(""�• f4.
<br /> ilon,70ta1 distance may be found by,
<br /> rule:the sbpe distance km
<br /> �r f'j `.of the nsp divided at twin' -
<br /> -- jr for a skgx distance 'S•.. taoced diet
<br /> ra372.2
<br /> w
<br />
|