|
y � , j•� fir
<br />TRIGONOMETRIC FORMULfE Iw.
<br />$ B B �:
<br />c a c a c
<br />s j C a
<br />f
<br />A b ftCAb CA
<br />Right Triangle 4 r Oblique Triangles
<br />—Solution of Right Triangles
<br />For Angle A, sin'=" l�` , cos = � tan = b cot = a , sec cosec = c
<br />Given ' Required
<br />a, b A, B"c tan A = b = cot B, c = a2 —+b2 = a 1 { as
<br />} a z
<br />5 Ang1
<br />ar c
<br />A, B,I b
<br />sin A = e = cos B, b = � (o+a) (c—a) = e � 1— u a
<br />}tl
<br />t
<br />Aa
<br />B "b, Jc
<br />B=90'=A; b.= a cots, c= a
<br />i '
<br />�
<br />sin A.
<br />f A, b
<br />B, a,'c
<br />B= 90°=A, a= b tan A, c= b
<br />`` cos A.
<br />A, c
<br />B, a, b
<br />B = 90°—A, a = e sin A, b = c cos A,
<br />Solution
<br />of Oblique Triangles
<br />i Given
<br />A, B, a
<br />Required
<br />b, c, C
<br />,a sin B in
<br />b = ' C = 180°—(A + B), c =
<br />sin A sin A
<br />A, a, b
<br />B, e, CC
<br />b sin A a sin C
<br />= 180°—(A + B), c =
<br />sin A
<br />a, b, C
<br />. A, B, e
<br />A f B=180°— C, tan (A—B)= (a -b) tan (A+B)
<br />ci + b ,
<br />a sin C
<br />� c=
<br />sin A
<br />b e
<br />A, B C
<br />s=a+b �c 1
<br />— ,ein �A=
<br />N(s--b)(s—c)
<br />2 be ,
<br />sinzB=a2(� )—
<br />,C=180°(AiB)
<br />{ a, b, e '
<br />Area
<br />s _ 2 , area = s (s—a (s—) (s—o)
<br />1
<br />A, b, c
<br />Area
<br />b e sin A
<br />area. =
<br />2'
<br />{,
<br />A, B, C,a
<br />Area
<br />�j a$ sin B sin C
<br />area =
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />e Cosine ofthe vertical angle. Thus: slope distance =319.4ft.
<br />a�stat'e
<br />Vert. angle=5' 101. From Table, Page IX. cos 51 101=
<br />I ,oQe
<br />e
<br />y .9%9. Horizontal distance=319.4X.9959=318.09 ft.
<br />la Horizontal distance also =Slone distance minus slope
<br />ve • distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ring result is obtained. Cosine 50 101=.9959.1—.9959=.0041.
<br />When the rise is known, the hori00ontal distance is approximately:—tbe 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=302.28 ft.
<br />2 X 302.6
<br />MADE IN U. 8. A.
<br />.KwR"91Ff�A7•�'iiliYlP4Si713"��
<br />
|