Question

To travel from Pottstown to Cogsville, a man drives his car 92 miles due east on one road, and then 15 miles due north on another road. describe the path that a bird could fly in a straight line from pottstown to cogsville. what angle does the line make with the two roads that the man used?

Answer 1

The bird's path forms an angle of 9.3° with the first (driving east) road and an angle of 80.7° with the second (driving north) road

Explanation:

Let

A ----> Pottstown

C ----> Cogsville

B ----> the intersection of the two roads

In this problem we have that the two roads are perpendicular

(Remember that North and East are perpendicular axis)

so

see the attached figure to better understand the problem

we know that

The path that a bird could fly in a straight line from Pottstown to Cogsville is the segment AC

so

Find the measure of angle A

In the right triangle ABC

`tan(A)=(BC)/(AB)` ----> by TOA (opposite side divided by the adjacent side)

substitute the given values

`tan(A)=(15)/(92)`

`A=tan^(-1)((15)/(92))=9.3^o`

Find the measure of angle C

In the right triangle ABC

we know that

The sum of the angle A and the measure of angle C is 90 degrees , because are complementary angles

`A+C=90^o`

we have

`A=9.3^o`

substitute

`9.3^o+C=90^o`

`C=80.7^o`

therefore

The bird's path forms an angle of 9.3° with the first (driving east) road and an angle of 80.7° with the second (driving north) road