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° = five sevenths. 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? 5 miles 7.4 miles 10 miles 19.6 miles

Answer 1

Answer:

Car B have to travel 10 miles on First Street to get to Oak Street

Step-by-step explanation:

Refer the attached figure.

First street = AB

Main Street = BC = 14 miles

Oak street = AC

We are also given that The intersection of Main Street and Oak Street forms a y° angle, and $tan y^{\circ} = \frac{5}{7}$

We will use trigonometric ratio

$\frac{Perpendicular}{Base}=Tan \theta$

So, $\frac{AB}{BC}=tan y$

$\frac{AB}{14}=\frac{5}{7}\\AB=\frac{5}{7} \times 14\\AB=10$

Hence Car B have to travel 10 miles on First Street to get to Oak Street