Question

question 6 (multiple choice worth 1 points) (05.03r hc) 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° = 7/5. 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. 15 miles 20 miles 25.4 miles 29.4 miles

Explanation:

Step1: Recall the tangent function formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Let the distance car \(A\) travels on Main Street be the opposite side (\(y = 21\) miles) and the distance car \(B\) travels on First Street be the adjacent side (\(x\)). We know that \(\tan x^{\circ}=\frac{7}{5}\).

Step2: Set up the proportion

Since \(\tan x^{\circ}=\frac{\text{distance on Main Street}}{\text{distance on First Street}}\), we have \(\frac{7}{5}=\frac{21}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(7x = 5\times21\). Then \(7x=105\). Divide both sides by \(7\): \(x=\frac{105}{7}=15\).

Answer:

A. 15 miles