|
r`
<br />sia A sin A
<br />W / �"-36
<br />I
<br />r- 1A, a, b
<br />B, c, C
<br />b sin A asin C
<br />sin B = , C = 180°—(A { B) , o =
<br />_
<br />a sin A
<br />lc 1Q�
<br />A. B. c
<br />A+B=1$0°— C, tan (A—B)�
<br />TRIGONOMETRIC FORMUL}R
<br />a
<br />z .A 6 CA�b CA c
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />a For Angle A. sin = , cos= b ,.tan= a , cot = b , sec = �, cosec = e
<br />l a b a
<br />Uiven Required ryz
<br />a, b A, B,a tan A = b _= cot B, o = a2 + s = a I f
<br />z
<br />a, a A. B, b
<br />a
<br />A. a iTi, b, a B=90°—A, b = a cotA, c= sin A. .
<br />a
<br />A, b B, a, o B=90'—A, a = b tan A, o= coe A.
<br />A, e, B, a, b B = 90°—A, a = o sin A, b�= a cos A,
<br />Solution of Oblique Triangles c.f,
<br />IA,B,a
<br />' �Qlven Required, b asin B � C = T$0°—(A + B), c = &ein C
<br />.b c,C
<br />sia A sin A
<br />I
<br />r- 1A, a, b
<br />B, c, C
<br />b sin A asin C
<br />sin B = , C = 180°—(A { B) , o =
<br />_
<br />a sin A
<br />A. B. c
<br />A+B=1$0°— C, tan (A—B)�
<br />a + b
<br />a sin C.
<br />'r
<br />c=
<br />sin A
<br />-
<br />b, a
<br />A, B, C
<br />s=a+Z+e,sinJA=
<br />Y h(c�e)I
<br />,C-180°—(A+B)
<br />a+b -l- e
<br />a; b, c
<br />Areas
<br />= 2 s— ) (s—c)
<br />d
<br />A; b, c
<br />Area
<br />area = b 6 sin A
<br />!
<br />2
<br />as sin B sin C
<br />$ B C, a
<br />1 I
<br />Area
<br />area -
<br />sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance=319.4ft
<br />ale �at+oe
<br />Vert. ansle=5° IM From Table, Page iX. cos 5l 10'=
<br />Horizontal distance=319,4X.9959=31&09 ft
<br />a
<br />5,ope
<br />ogle
<br />p'
<br />w8959.
<br />Horizontal distance also —Slope distance minus slope
<br />a
<br />�e
<br />distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance
<br />Ing result is obtained. Cosine 5° 101=.9959.1—.9959=.0041.
<br />819.4X.0041=1.91. 819.4-1.31=318.09 ft.
<br />i
<br />When the=rise is known, the horizontal distance is approximately:—the slope dist-
<br />]
<br />`4ce less the square of the rise divided by twice the slope distance. Thus: rise -i4 ft;
<br />y'
<br />&lope distance=302.6It.
<br />Horizontal d1stance=302.0— 14 X 14 =3026—a32=30228 f't
<br />s
<br />2 X 9026 --
<br />MADE In V. a- A. •
<br />
|