SOLUTION: A surveyor is mapping a triangular field. From one corner he sights between the two opposite corners and finds an angle of 46°. He knows that the length of the opposite sid

Algebra ->  Trigonometry-basics -> SOLUTION: A surveyor is mapping a triangular field. From one corner he sights between the two opposite corners and finds an angle of 46°. He knows that the length of the opposite sid      Log On


   

Question 889258: A surveyor is mapping a triangular field. From one corner he sights between the two opposite
corners and finds an angle of 46°. He knows that the length of the opposite side of the field is 60m
while the side to his left is 70m. The surveyor creates one drawing of the field and sends the single
drawing and a bill to the client. Should the client pay the bill? Explain
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
The surveyer can draw a triangle with 60 m side opposite the 46 degree angle,
the 70 m side opposite angle b,
and the unknown side C opposite of angle c.

Law of Sines allows:
60%2Fsin%2846%29=70%2Fsin%28b%29;
C%2Fsin%28c%29=60%2Fsin%2846%29;
46%2Bb%2Bc=180 degrees.

If the surveyer only labels 70 m, 60 m, and the 46 degree angle, and does nothing more, then
he has not done enough of his job. What he still ought to do is....
sin%28b%29%2F70=sin%2846%29%2F60
sin%28b%29=%287%2F6%29sin%2846%29
highlight%28b=arcsin%28%287%2F6%29sin%2846%29%29%29---needs computaion
-
c=180-46-b
c=180-46-arcsin%28%287%2F6%29sin%2846%29%29---needs computation
and then
C%2Fsin%28c%29=60%2Fsin%2846%29
highlight%28C=60%2Asin%28c%29%2Fsin%2846%29%29---needs computation
-
He NEEDS to compute b, c and C. With these finished computations, he can finish labeling the triangular field diagram.