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 First Street and Oak Street forms an x° angle, and tan x° = seven fifths. 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? Round your answer to the nearest hundredth of a mile.

7.14 miles
14 miles
20 miles
28.14 miles

Answer 1

The distance car B will have to travel on Main Street to get to Oak Street is approximately 7.14 miles.

Therefore, the correct answer is: option "7.14 miles".

Step-by-step explanation:

To solve for the distance that car B will have to travel on Main Street to get to Oak Street, we can use the concept of right triangles and trigonometric functions.

Since the tangent of x° is equal to seven fifths, we can use the inverse tangent function to find the value of x°.

=> tan-1(7/5)

≈ 53.13°.

With this information, we know that the angle between First Street and Oak Street is 53.13°.

Since First Street and Main Street form a right angle, the angle between Main Street and Oak Street is:

= 90° - 53.13°

= 36.87°.

Let's call the distance that car B will have to travel on Main Street as d.

We can use the tangent function to set up the following equation: tan(36.87°) = d / 10 miles.

Solving for d, we find that d ≈ 7.14 miles.