Question

To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible.

If the distance from the EDM to the towns is 4.2 miles and 4 miles and the angle between the two lines of sight is 69 degrees, find the distance between the towns to the nearest tenth of a mile.

Answer 1

Answer:

4.6 miles

Step-by-step explanation:

-Since we are given 2 sides and an included angle, we use the Cosine Rule to calculate the distance between the two towns.

-69° is the angle corresponding to the the distance between the two towns;

$a^2=b^2+c^2-2bc Cos \ A\\\\a^2=4.2^2+4^2-2(4.2)(4.0)\ Cos \ 69\textdegree\\\\=21.599\\\\a=\sqrt{21.599}\\\\=4.647 \ miles$

$\approx4.6\ miles$

Hence, the distance between the towns is 4.6 miles