Question

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.​

Answer 1

`\approx 118.4`

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=√(44909-40940cos(41))`

`c \approx 118. 4`