A water tower is located x = 375 ft from a building (see the figure). From a window in the building, an observer notes that the angle of elevation to the top of the tower is 39° and that the angle of depression to the bottom of the tower is 25°.
How tall is the tower? (Round your answer to the nearest foot.)
I belive the answer is 304 bc I did 375Tan(39°) and got 303.66 but it marked it wrong can someone help me
the height of the observer is
... h = 375 sin(25º)
the height of the tower above the observer is
... h = 375 sin(39º)
add the two heights to find the tower
(remember to round)
To find the height of the tower, you can use the tangent function. However, when using the tangent function, it's important to make sure that the angle is relative to the same side of the triangle.
In this case, the angle of elevation is relative to the observer in the building, so it is the opposite angle to the height of the tower. On the other hand, the angle of depression is relative to the observer in the tower, so it is the opposite angle to the depth of the tower. So, we need to use the tangent function with the angle of depression.
Let's first find the depth of the tower using the angle of depression:
tan(25°) = height of tower / distance to tower
We know the distance to the tower (375 ft), so let's solve for the height:
height of tower = tan(25°) * 375 ft
height of tower ≈ 166.35 ft
Now, to find the total height of the tower, we need to add the height above the ground level (166.35 ft) to the depth of the tower. However, notice that the height and depth are on opposite sides of the building, so they have opposite signs. Therefore, we subtract the depth from the height:
total height of the tower = |height above ground| - |depth below ground|
total height of the tower = |166.35 ft| - |166.35 ft|
total height of the tower = 166.35 ft - 166.35 ft
total height of the tower ≈ 0 ft
In this case, the total height of the tower is approximately 0 ft. Double-check your calculations to ensure accuracy.
To find the height of the tower, we need to use trigonometry.
Let's start by drawing a diagram to visualize the problem. We have a water tower and a building. The angle of elevation from the window to the top of the tower is 39°, and the angle of depression from the window to the bottom of the tower is 25°.
_____________ <- Water tower top
| |
| Building |
| |
|______________| <- Water tower bottom
^ ^
| |
angle of angle of
elevation depression
Now, let's label the relevant quantities:
- The distance from the building to the tower is x = 375 ft.
- The height of the tower is h (what we want to find).
We can use the tangent function to relate the angle of elevation to the height of the tower. The tangent of the angle of elevation is equal to opposite/adjacent, which gives us:
tan(39°) = h/x
So, we can rearrange this equation to solve for h:
h = x * tan(39°)
Plugging in the given values, we have:
h = 375 * tan(39°)
h ≈ 304 feet
Therefore, the height of the tower is approximately 304 feet.
It seems like you did the calculations correctly, so it's possible that there was a rounding error. Ensure that you are using a calculator that provides accurate trigonometric functions, and round your answer to the nearest foot as requested in the question.