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<br />TRIGONOMETRIC FORMULtE
<br />J1 B
<br />a a
<br />4 I ` � � � �rr� off. _' � 4 .A �1 L' f •
<br />MIght Tia -Triangles
<br />ue 1
<br />.,,�y i� .. !'✓� �'ti3l r f� ' I `� { Solution of -Right Triangles
<br />qq'•
<br />f1 }} For Angle A. sin _ C. ,cos — =c ,ten= b ,cot — a ,secb,,, �asec = a
<br />Required
<br />A, B ,otanA'-= n — cot = 'i =_a 1 bz
<br />. A B, b sin A=.�=cos B�b=�(c
<br />XI
<br />A, 4 $, b, a B=90°—A b = acotA, c= a f �> .k
<br />le ein A.
<br />,7`. 49 ` -,�- A� , 'B, a, a B=90°—A`,a - btan d,c= A
<br />Al
<br />' � A,c }B, a_&B=90 —A,a = esin'A, b=`c cos A,? , ` Solution of. Oblique Triangles
<br />''Given Required b a sin B . C =.180°—/A B c = a sin _C
<br />,ba /j - `\ -f �7 7. �u `. 1 sin A sin A
<br />-- r ``
<br />L� b sin A ° ( a sin C
<br />3 q A a+.b..' B e C sing= 4 ,C=1$0—A: {-B),c= sin
<br />�j,!� b, C A, B, c A8=1$0°— C, taa(A—B)= (a—b) tan. (A } 13y
<br />�� ° �°1 -1 a + b
<br />sin
<br />o—
<br />sin A
<br />J 7/L ti {•.. 6 p8 r n:..�a,'b, a A, b, C 3--,sin-21A=
<br />,sinsA=� be i
<br />7i3 yT sin,B=1�(.r—aa(s� c)'C=180°—(A+B)
<br />i
<br />a1 b �c
<br /># - % 7.
<br />a," b; c' ' Areas = 2 ,area (s—b) (s—c
<br />r7' fi /si 0 ( A, b, c Area area — h c s24 A
<br />o i
<br />"' Q 42 sin B sin C t
<br />G n; Area area =
<br />2 ,sin A
<br />_ VV REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />p O e cosine of the vertical angle. Thus: slope distance =319.4 ft. e
<br />�Onil
<br />c 9959.Holrixontal distanc01. e19.4TableX.9959e38.09 ft IX. Cos 5° ]0'—
<br />gle Horizontal distance also=Slope distance minus slope
<br />i distance times (1—cosine of vertical angle)• With thesame figures as in the preceding example, the follow -
<br />v_ ,. Horizontal distance ing result is obtained. Cosine 5° 101=.9959.1—.9959=.0041.
<br />� 519.4X,OOt1=1.31. 319.4-1.31=318.09 ft.
<br />i ! When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />I ince less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft., d!
<br />Ij14 X 14
<br />slope distance=302.0 ft Horizontal distanee=3020— —3028-0.32=302.28 fl.
<br />—� -- �— 2X3026
<br />- MADE IN U. G. A.
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