A road is inclined at an angle of 6°. After driving 5,440 feet
along this road, find the driver's increase in altitude. Round to
the nearest foot.
The driver's increase in
altitude is ____ ft.
A. 5,410
B. 569
C. 52,043
D. 572
Answers
========================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(6) = a/5440
5440*sin(6) = a
a = 5440*sin(6)
a = 568.634840176034
a = 569 feet, which shows why choice B is the answer.
This value is approximate. Make sure your calculator is in degree mode. One way to check is to compute sin(30) and you should get 0.5
side note: 569 feet is roughly equal to 0.1078 miles.
The driver's increase in altitude is 569 feet.
Given that,
A road is inclined at an angle of 6°.
After driving 5,440 feet along this road,
We have to determine,
The driver's increase in altitude?
According to the question,
A road is inclined at an angle of 6°.
After driving 5,440 feet along this road,
The inclination is determined by using the sin angle.
Therefore,
The driver's increase in altitude is,
[tex]\rm Sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\\[/tex]
Where Perpendicular = a, angle = 6 degree and hypotenuse = 5,440ft.
Substitute all the values in the formula,
[tex]\rm Sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\\\rm Sin6 = \dfrac{a}{5440}\\\\\rm 0.104= \dfrac{Perpendicular}{5440}\\\\Perpendicular = 5440 \times 0.104\\\\Perpendicular = 569 \ feet[/tex]
Hence, The driver's increase in altitude is 569 feet.
For more details refer to the link given below.
https://brainly.com/question/11280532
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