The post office is at the corner of First Street and Main Street, which forms a right angle. First Street intersects with Oak Street to the north, and Main Street intersects with Oak Street to the east. The intersection of Main Street and Oak Street forms a y° angle, and tan y° = 5/7. Car A drives on Main Street for 14 miles to arrive at Oak Street. How far will car B have to travel on First Street to get to Oak Street? Round your answer to the nearest tenth of a mile.

a. 5 miles
b. 7.4 miles
c. 10 miles
d. 19.6 miles

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Answer:

Option c

Step-by-step explanation:

We are given that the post office is at the corner of first street and main street and they form  right angled .

We have to find the distance travel by car B to reach Oak street from First street

Let x be the distance traveled by car B on First street to get to Oak street

In right angled triangle NOE

OE=14 miles

NO=x

[tex]tany^{\circ}=\frac{5}{7}[/tex]

[tex]tan\theta=\frac{opposite \;side\; of\; angle\; y}{adjacent\; side \;of\; y}[/tex]

[tex]\frac{5}{7}=\frac{x}{14}[/tex]

[tex]x=\frac{5\times 14}{7}[/tex]

[tex]x=10 miles[/tex]

Therefore, option c is true.

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Answer:

10 miles

Step-by-step explanation:

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