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elena-s [515]
3 years ago
5

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

oth 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.
Mathematics
1 answer:
crimeas [40]3 years ago
6 0

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

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