Question

To get from her house to school, Amy travels on one street for 2,550 meters. She then turns and travels on another street for 2,774 meters. This route is represented in the figure by the sequence of points K, L, M. According to the angle shown in the figure and the given information, what is the distance, to the nearest meter, from Amy's house to school represented by the line from K to M in the figure?

Answer 1

Okay, here we have this:

We need to calculate the distance from Amy's house to school represented by the line from K to M in the figure, so we are going to use the cosine law, we obtain the following:

$\begin{gathered} a^2=b^2+c^2-2\cdot b\cdot c\cdot\text{Cos(A)} \\ a^2=2550^2+2774^2-2\cdot2550\cdot2774\cdot\text{Cos(115)} \\ a=\sqrt{-14147400\cos\left(115^{\circ\:}\right)[phone]} \\ a\approx4492 \end{gathered}$

Finally we obtain that the distance, to the nearest meter, from Amy's house to school represented by the line from K to M in the figure is 4492 meters.