Question

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

Answer 1

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:

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

$c^2=44909-40940cos(41)$

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

$c \approx 118. 4$