Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve this problem, let's break it down step by step:
### Step 1: Understand the Given Information
- The post office is at the corner of First Street and Main Street, forming a right angle.
- First Street intersects with Oak Street to the north, and Main Street intersects with Oak Street to the east.
- Main Street and Oak Street form an angle [tex]\( y \)[/tex] where [tex]\( \tan(y) = \frac{5}{7} \)[/tex].
- A car drives on Main Street for 14 miles to arrive at Oak Street.
### Step 2: Solve for the Distance on First Street
We are given the tangent of the angle [tex]\( y \)[/tex], which is the ratio of the length of the opposite side to the adjacent side in a right triangle. Here:
[tex]\[ \tan(y) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{7} \][/tex]
In this scenario:
- The "opposite" side corresponds to the distance traveled on First Street.
- The "adjacent" side corresponds to the distance traveled on Main Street, which is 14 miles.
Let's denote the distance traveled on First Street as [tex]\( d \)[/tex].
Since [tex]\( \tan(y) = \frac{d}{14} \)[/tex], we set up the equation:
[tex]\[ \frac{d}{14} = \frac{5}{7} \][/tex]
To find [tex]\( d \)[/tex], we solve:
[tex]\[ d = 14 \times \frac{5}{7} \][/tex]
### Step 3: Calculate the Distance
Now, calculate the distance:
[tex]\[ d = 14 \times \frac{5}{7} = 14 \times 0.7142857142857143 \approx 10.0 \][/tex]
### Step 4: Round the Answer
Since the problem asks us to round the answer to the nearest tenth of a mile, we see that the calculated distance [tex]\( d \)[/tex] is already [tex]\( 10.0 \)[/tex].
### Step 5: Identify the Correct Option
The options are:
- 5 miles
- 7.4 miles
- 10 miles
- 19.6 miles
Given that our rounded distance is [tex]\( 10.0 \)[/tex] miles, the correct option is:
- 10 miles
Thus, car B will have to travel approximately 10 miles on First Street to get to Oak Street.
### Step 1: Understand the Given Information
- The post office is at the corner of First Street and Main Street, forming a right angle.
- First Street intersects with Oak Street to the north, and Main Street intersects with Oak Street to the east.
- Main Street and Oak Street form an angle [tex]\( y \)[/tex] where [tex]\( \tan(y) = \frac{5}{7} \)[/tex].
- A car drives on Main Street for 14 miles to arrive at Oak Street.
### Step 2: Solve for the Distance on First Street
We are given the tangent of the angle [tex]\( y \)[/tex], which is the ratio of the length of the opposite side to the adjacent side in a right triangle. Here:
[tex]\[ \tan(y) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{7} \][/tex]
In this scenario:
- The "opposite" side corresponds to the distance traveled on First Street.
- The "adjacent" side corresponds to the distance traveled on Main Street, which is 14 miles.
Let's denote the distance traveled on First Street as [tex]\( d \)[/tex].
Since [tex]\( \tan(y) = \frac{d}{14} \)[/tex], we set up the equation:
[tex]\[ \frac{d}{14} = \frac{5}{7} \][/tex]
To find [tex]\( d \)[/tex], we solve:
[tex]\[ d = 14 \times \frac{5}{7} \][/tex]
### Step 3: Calculate the Distance
Now, calculate the distance:
[tex]\[ d = 14 \times \frac{5}{7} = 14 \times 0.7142857142857143 \approx 10.0 \][/tex]
### Step 4: Round the Answer
Since the problem asks us to round the answer to the nearest tenth of a mile, we see that the calculated distance [tex]\( d \)[/tex] is already [tex]\( 10.0 \)[/tex].
### Step 5: Identify the Correct Option
The options are:
- 5 miles
- 7.4 miles
- 10 miles
- 19.6 miles
Given that our rounded distance is [tex]\( 10.0 \)[/tex] miles, the correct option is:
- 10 miles
Thus, car B will have to travel approximately 10 miles on First Street to get to Oak Street.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.