Question

question 7. 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° = 7/21. car a drives on main street for 21 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.

Explanation:

Step1: Recall tangent definition

The tangent of an angle in a right - triangle is defined as $\tan x=\frac{\text{opposite}}{\text{adjacent}}$. Let the distance car B travels on First Street be $y$ miles and the distance car A travels on Main Street be $x = 21$ miles. We know that $\tan x=\frac{7}{3}$, and in our right - triangle formed by the streets, $\tan x=\frac{y}{x}$.

Step2: Substitute values

Substitute $x = 21$ and $\tan x=\frac{7}{3}$ into the equation $\tan x=\frac{y}{x}$. We get $\frac{7}{3}=\frac{y}{21}$.

Step3: Solve for y

Cross - multiply: $3y=7\times21$. Then $3y = 147$. Divide both sides by 3: $y=\frac{147}{3}=49$.

Answer:

49 miles