Question

A surveyor stands a point B. She calculates the distance to point A to be 1 mile. Then she calculates the distance from B to C to be 3 miles. If the angle between the path from B to A and from B to C is 32°, determine the distance from A to C. Round your answer to the nearest tenth and label your answer.

Answer 1

We can draw a triangle with the information givene as:

We have to find the distance AC.

In this case, we can apply the law of cosines as:

$AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot\cos (B)$

Replacing with the information given, we can calculate AC as:

$\begin{gathered} AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot\cos (B) \\ AC^2=1^2+3^2-2\cdot1\cdot3\cdot\cos (32\degree) \\ AC^2\approx1+9-6\cdot0.848 \\ AC^2\approx10-5.088 \\ AC^2\approx4.912 \\ AC\approx\sqrt[]{4.912} \\ AC\approx2.2 \end{gathered}$

Answer: the distance AC is 2.2 miles.