|
7
<br />TRIGONOMETRIC FORMULlE
<br />C B
<br />° a a c a
<br />i A b C A b C A b C
<br />�.' Right Triangle Oblique Triangles
<br />SoIution of Right Triangles
<br />For Angle A, sin = a , cos = c b , tan = a ; cot = b a , sec = , cosec = a
<br />� c b b � a
<br />f Given Required!
<br />2
<br />a,b A,B,c tanA=b=cotB,c= a2+ 2—a 1 } 2z
<br />( i a, c A, B, b sin A = a =cos B, b = c a c—a a2
<br />1 A, a B, b, c 8=90°—A, b = a cotA., 0— 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 B = 90°l= A' a = c sin A, b= e cos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />A, B a b, c, C b = a sin B C, = 180°—(A + B), c = 'sin C
<br />sin .A ' sin A
<br />b sin Aa 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=130°— C, tan z (A—B)= (a—b) tan' (A+B)
<br />a + b '
<br />c=
<br />a sin C
<br />sin A
<br />t a, b, c A, B, Cs=a+2+c,sin 2A=�(s— a(cs—c),
<br />�,I
<br />sinzB=V( ac ),C=180°—(A+B)
<br />a+2
<br />-I- c
<br />b, c Area s = 2 ' , area = 1/s(s—a (s—b) (s—c
<br />area rea c , b
<br />,
<br />Ab e sin A
<br />= 2'
<br />:• area = a2,sin B sin C
<br />A, B, C, a Area
<br />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 />tem°c Vert. angle=50 101. From Table, Page IX. cos 50101=
<br />' e ass y 9959. Horizontal distance=319.4X•9959=318.09 ft.
<br />5�°p • An��e Horizontal distance also =Slope distance minus slope
<br />e t• 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 5° 10'=.0959.1—.9959=.0041.
<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=302.6— 14 X 14 =302.6-0.32=302.28M
<br />2 X 302.6
<br />MADE IN D. $.A.
<br />
|