you are standing 15 feet from a statue the angle of the elevation from eye level to the top of the statue is 27 degrees, and the angle of depression to the base of the statue is 18 degrees. How tall is the statue? show work
H1=15 tan(27°) [angle of elev.]
H2=15 tan(-18°) [angle of depression, <0]
Height
=H1-H2
=15(tan(27°)-tan(-18°))
12.516
To find the height of the statue, we can use trigonometry.
Let's consider the right-angled triangle formed with the statue as the vertical side, the distance from the statue to the observer as the horizontal side, and the observer's eye level as the hypotenuse.
Step 1: Determine the height of the observer's eye level above the ground.
Since we are given the angle of depression, which is the angle between the horizontal and the line of sight downward, we subtract this angle from 90 degrees to find the angle of elevation. In this case, the angle of elevation is 90 degrees - 18 degrees = 72 degrees.
Step 2: Find the distance from the statue to the observer.
We are given this distance as 15 feet in the problem statement.
Step 3: Calculate the height of the statue using the tangent function.
The tangent of an angle is calculated as the ratio of the opposite side to the adjacent side.
In this case, we have the opposite side (height of the statue) and the adjacent side (distance from the statue to the observer). We can use the tangent of the angle of elevation to solve for the height of the statue.
Using the formula: tan(angle) = opposite / adjacent
tan(72 degrees) = height / 15 feet
To solve for the height, rearrange the equation:
height = tan(72 degrees) * 15 feet.
Now we can find the height using a scientific calculator or online calculator, which gives us:
height = tan(72 degrees) * 15 feet ≈ 45.67 feet.
Therefore, the height of the statue is approximately 45.67 feet.