A tower casts a shadow 22 feet long. If the angle of depression lookig down from the top of the tower to the tip of the shadow is 14 degrees, what is the height of the tower
height/22=cosine 14
height=22cos14
To find the height of the tower, we can use trigonometry and the tangent function.
The angle of depression is the angle between the horizontal and the line of sight from the top of the tower to the tip of the shadow. In this case, the angle of depression is 14 degrees.
We can use the tangent function to find the height of the tower:
tan(angle of depression) = height of the tower / length of the shadow
Substituting the given values:
tan(14 degrees) = height of the tower / 22 feet
To find the height of the tower, we can rearrange the equation:
height of the tower = tan(14 degrees) * 22 feet
Using a calculator to find the tangent of 14 degrees:
tan(14 degrees) ≈ 0.2493
Multiplying this value by the length of the shadow:
height of the tower ≈ 0.2493 * 22 feet
Calculating the approximate height of the tower:
height of the tower ≈ 5.48 feet
Therefore, the approximate height of the tower is 5.48 feet.