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Part A
Technology required. A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally.
How high is the plane at the time?
If necessary, round your answer to the nearest tenth.
Do not include units (miles) in your answer.
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Hint
Draw and label a right triangle with the given information. The angle of elevation is the angle REPORT THIS HINT
that the flight path makes with the ground.
Hint
Using the length of the plane's flight path and the 6 degree angle, decide which
REPORT THIS HINT
trigonometric function to use to find the height of the plane. Set up and solve an equation
using that trigonometric function.

Verified Answer :

GinnyAnswer

To solve this problem, let's follow these steps:

1. Understand the problem:
- The angle of elevation (from the ground to the plane's flight path) is 6 degrees.
- The plane travels 10 miles horizontally from its initial take-off point.

2. Draw a right triangle:
- The horizontal distance (adjacent side to the angle) is 10 miles.
- We need to find the vertical distance (height of the plane, which is the opposite side to the angle).

3. Choose the appropriate trigonometric function:
- Given angle \(\(\theta\)\), opposite side (height), and adjacent side (horizontal distance), we use the tangent function:
\(\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]\)

4. Set up the equation:
- \(\(\theta = 6\)\) degrees
- \(\(\text{adjacent} = 10\)\) miles
- \(\(\tan(6^\circ) = \frac{\text{height}}{10}\)\)

5. Solve for the height:
- Rearrange the equation to solve for height:
\(\[ \text{height} = 10 \times \tan(6^\circ) \]\)

6. Convert angle from degrees to radians:
- Since trigonometric functions typically use radians, convert \(\(6\)\) degrees to radians:
\(\[ 6^\circ = 0.1047 \text{ radians} \quad (\text{approximately}) \]\)

7. Calculate height using the tangent function:
- \(\(\tan(0.1047) \approx 0.1051\)\)
- So,
\(\[ \text{height} = 10 \times 0.1051 \approx 1.051 \]\)

8. Round to the nearest tenth:
- \(\(1.051\)\) rounded to the nearest tenth is \(\(1.1\)\).

Therefore, the height of the plane is 1.1.

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