From the top of an 8m house the angle of elevation to the top of the schools flagpole across the street is 9 degrees
The angle of depression is 42degrees to the bottom of the pole
How tall is the flagpole
To find the height of the flagpole, we can use the tangent of the angle of elevation.
Let's call the height of the flagpole "x".
Using the tangent function:
tan(9 degrees) = x / 8m
Rearranging the equation to solve for x:
x = tan(9 degrees) * 8m
Calculating the value:
x ≈ 1.53 * 8m
x ≈ 12.23m
Therefore, the height of the flagpole is approximately 12.23 meters.
To find the height of the flagpole, we can use trigonometry.
Let's consider the right triangle formed by the house, the flagpole, and the line of sight from the top of the house to the top of the flagpole. The angle of elevation (9 degrees) is the angle between the line of sight and the horizontal line. The height of the house (8m) is the opposite side of this angle.
Similarly, the angle of depression (42 degrees) is the angle between the line of sight from the top of the house to the bottom of the flagpole and the horizontal line. We need to remember that the bottom of the flagpole acts as the opposite side in this case.
So, using trigonometry, we can set up the following equation:
tan(9 degrees) = height of the flagpole / 8m
By rearranging the equation, we can solve for the height of the flagpole:
height of the flagpole = tan(9 degrees) * 8m
Calculating this using a calculator, the height of the flagpole is approximately 1.28m. Therefore, the flagpole is approximately 1.28 meters tall.
as always, draw a diagram.
The distance d between the house and pole is
d = 8cot42°
Now you can see that the height of the pole is
8 + d tan9°