|
- TRIGONOMETRIC FORMULfE
<br />B B
<br />c ac a c a
<br />A b C A b C A b C
<br />Right Triangle f Oblique Triangles
<br />f Solution of Right Triangles
<br />For Angle A. sin = a , cos = b , tan = a , cot = b , sec = o , cosec =
<br />c c b a b a
<br />Given Required
<br />a,6 A,B,c taaA=b= cot B,c= a2+ s=a 1+Qz
<br />- a, c A, B, b sin A = o = cos B, b = \/ (c+a) (c—a) =c 1— o
<br />A, a B, b, c B=90°—A, b= a cot A, c= a
<br />sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />A, c B, a, b I B =900—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />A B, a b, c, C b = a sin B G, = 180°—(A +-B), c = asin C
<br />sin A ' sin A
<br />b sin A a sin C
<br />A, a, b B, c, C sin B =a , C = 180°—(A + B) , c = sin A
<br />a, b, C A, B, c A+B=180°— C, tan ; (A—B)= (a—b) tan (A+B)�
<br />a + b
<br />=a sin C
<br />c
<br />sin A
<br />i. a, b, c A, B, C &—a+Z+c,sin'jA=.\1I b c c),
<br />sin;B= (s—a)—),C=180°—(A+B)
<br />a+b+c V
<br />a, b, c Area s= 2 , area = s(s—a s— (a—c
<br />A, b, c Areab c sip A
<br />1 area = 2
<br />1 n a= sin B sin, C
<br />A, B, C, a Area 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 />�sppe Vert. angle= 50 101. From Table, Page 1X. cos 50 1p'=
<br />0 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />glop Anglc Horizontal distance also= Slope distance minus slope
<br />- 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 51 101=.9959.1—.9959=.0D41.
<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=302.6 ft. Horizontal distance=3026— 14 X 14 ==6-0.32=302.28 ft.
<br />2 X 302.6
<br />MADE IN U. 8. A.
<br />
|