2 Technology required. A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally. a. How high is the plane at the
Mathematics
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Question
2
Technology required. A plane leaves the ground with an elevation angle of 6 degrees.
The plane travels 10 miles horizontally.
a. How high is the plane at the time?
b. What is the distance of the plane's path?
Round answers to the nearest tenths.
How high is the plane at this time?
miles
What is the distance of the plane's path?
miles
Technology required. A plane leaves the ground with an elevation angle of 6 degrees.
The plane travels 10 miles horizontally.
a. How high is the plane at the time?
b. What is the distance of the plane's path?
Round answers to the nearest tenths.
How high is the plane at this time?
miles
What is the distance of the plane's path?
miles
1 Answer

1. User Answers vintechnology
The height of the plane at that time is 1.1 miles
The distance of the plane's path is 10.1 miles
The situation forms a right angle triangle.
Using trigonometric ratio,
tan 6° = opposite / adjacent
The height of the plane is the opposite side of the triangle. The adjacent
side is the distance travelled horizontally. Therefore,
tan 6° = h / 10
cross multiply
h = 10 tan 6°
h = 10 × 0.10510423526
h = 1.05104235266
height of the plane at that time = 1.1 miles
The distance of the plane path is the hypotenuse of the triangle formed.
Therefore,
c² = a² + b²
c² = 10² + 1.1²
c = √101.21
c = 10.0603180864
c = 10.1 miles
plane's path = 10.1 miles
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