Erica is participating in a road race. The first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25
∘ north of east. The road then turns due north for another 3.0 mi to the finish line. In miles, what is the straight-line distance from the starting point to the end of the race? Express your answer in miles.
1 answer:
Answer:
6.79 miles
Step-by-step explanation:
Consider triangle ABC where A marks the starting point and C indicates the end point.
|AB|=5.2 miles
|BC|=3.0 miles
∠ABC = 90 + 75 = 165°
We're given two side lengths and an angle that is not opposite to either side.
The approach to resolve this scenario is known as the Cosine Rule.
Each side opposite an angle is designated by the corresponding lowercase letter.
The Cosine Rule asserts that:
b² = a² + c² - 2acCosB
|AC|²=3² + 5.2² - (2 × 5.2 × Cos 165°)
|AC|²=9 + 27.04 + 10.05
|AC|²=46.09
|AC|=√46.09=6.79 miles
Thus, the straight-line distance from A to C measures 6.79 miles
You might be interested in
Answer:
(C) They have the same coefficient of variation
Step-by-step explanation:
The coefficient of variation (CV) is calculated using the formula:
Where represents standard deviation and
represents the mean.
Bob's average weight is 200 pounds with a standard deviation of 16 pounds
This indicates that .
Thus, his coefficient of variation is
Mary's average weight is 125 pounds, with a standard deviation of 10 pounds.
This implies
Therefore, her coefficient of variation is
Since both have the same coefficient of variation, the accurate response is.
(C) They have the same coefficient of variation