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ELEN [110]
3 years ago
7

A surveyor in a canyon takes measurements and draws the diagram shown.

Mathematics
1 answer:
Fiesta28 [93]3 years ago
5 0

Answer:

\approx 118.4

Step-by-step explanation:

We know two sides and the angle between the sides, so we can use the Law of Cosines. Recall that the Law of Cosines states that:

c^2=a^2+b^2-2abcos(C), where a and b are the sides and C is the angle in between.

Let's substitute 115 for a, 178 for b, and 41 for Angle C.

Thus:

c^2=115^2+178^2-2(115)(178)cos(41)

c^2=44909-40940cos(41)

c=\sqrt{44909-40940cos(41)}

c \approx 118. 4

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