The post office is at the corner of First Street and Main Street, which forms a right angle. Fist Street intersects with Oak Street to the north, and Main Street intersects with Oak Street to the east. The intersection of First Street and Oak Street forms an x* angle, and tan x* = 7/. Car A drives on First Street for 10 miles to arrive at Oak Street. How far will car B have to travel on Main Street to get to Oak Street?

             

Explanation:

From the description:

First Street and Main Street form a right angle (given)Say First Street is vertical, then Main Street is horizontal: they are the two legs of a right triangle.Oak Street intersects both First Street and Main Street (given), then it is over the hypotenuse of the right triangle.The tangent of the angle between Oak Street and First Street is 7/5 (given).

The trigonometric function tangent is equal to opposite leg divided by the adjacent leg.

Car A drives on First Street for 10 miles to arrive at Oak Street: implies that First Street is the adjacent leg to the angle xº.How far will car B have to travel on Main Street to get to Oak Street?: Main Street is the opposite leg to angle xº. Call M this length of this leg.

Then, in the right triangle you know the tangent of an angle and its adjacent leg, which lets you to determine the other leg.

Therefore: