Answer :
To determine the height of the plane above the ground after it has traveled 10 miles horizontally with an elevation angle of 6 degrees, follow these steps:
1. Convert the Elevation Angle to Radians:
Angles in trigonometric functions like tangent are typically expressed in radians. To convert the degrees to radians:
[tex]\[ \text{elevation\_angle\_radians} = 0.10471975511965978 \][/tex]
2. Calculate the Height Using the Tangent Function:
The tangent of the elevation angle gives the ratio of the height (opposite side) to the horizontal distance (adjacent side):
[tex]\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Rearranging to solve for height (opposite side):
[tex]\[ \text{height} = \tan(\text{elevation\_angle}) \times \text{horizontal\_distance} \][/tex]
Substitute the known values:
[tex]\[ \text{height} = \tan(0.10471975511965978) \times 10 \][/tex]
[tex]\[ \text{height} = 1.0510423526567647 \][/tex]
3. Round the Height to the Nearest Tenth:
The final step is to round the height to the nearest tenth:
[tex]\[ \text{height\_rounded} = 1.1 \][/tex]
So, the height of the plane after traveling 10 miles horizontally at an elevation angle of 6 degrees is [tex]\( \boxed{1.1} \)[/tex].
1. Convert the Elevation Angle to Radians:
Angles in trigonometric functions like tangent are typically expressed in radians. To convert the degrees to radians:
[tex]\[ \text{elevation\_angle\_radians} = 0.10471975511965978 \][/tex]
2. Calculate the Height Using the Tangent Function:
The tangent of the elevation angle gives the ratio of the height (opposite side) to the horizontal distance (adjacent side):
[tex]\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Rearranging to solve for height (opposite side):
[tex]\[ \text{height} = \tan(\text{elevation\_angle}) \times \text{horizontal\_distance} \][/tex]
Substitute the known values:
[tex]\[ \text{height} = \tan(0.10471975511965978) \times 10 \][/tex]
[tex]\[ \text{height} = 1.0510423526567647 \][/tex]
3. Round the Height to the Nearest Tenth:
The final step is to round the height to the nearest tenth:
[tex]\[ \text{height\_rounded} = 1.1 \][/tex]
So, the height of the plane after traveling 10 miles horizontally at an elevation angle of 6 degrees is [tex]\( \boxed{1.1} \)[/tex].
