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A surveyor in a canyon takes measurements and draws the diagram shown.
Determine the length of a bridge that would stretch across the canyon to 1 decimal
place.​

A surveyor in a canyon takes measurements and draws the diagram shownDetermine the length of a bridge that would stretch across the canyon to 1 decimalplace class=

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xKelvin

Answer:

[tex]\approx 118.4[/tex]

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:

[tex]c^2=a^2+b^2-2abcos(C)[/tex], 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:

[tex]c^2=115^2+178^2-2(115)(178)cos(41)[/tex]

[tex]c^2=44909-40940cos(41)[/tex]

[tex]c=\sqrt{44909-40940cos(41)}[/tex]

[tex]c \approx 118. 4[/tex]

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