Question

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

Answer 1

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

$tany^{\circ}=\frac{5}{7}$

$tan\theta=\frac{opposite \;side\; of\; angle\; y}{adjacent\; side \;of\; y}$

$\frac{5}{7}=\frac{x}{14}$

$x=\frac{5\times 14}{7}$

$x=10 miles$

Therefore, option c is true.