A pole sits on top of a tall building an observer on ground 17 m away from building finds the angle of elevation to the base of the pole to be 30 degrees and the angle of elevation to top of pole to be 45 degree. Find height of pole to nearest tenth. Draw a pic
I assume you made the diagram.
height to top of building:
h1/17 = tan30
h1 = 17tan30
height to top tower:
h2/17 = tan45
h2 = 17tan45
tower = h2 - h1
take over, let me know what you get
17- 17sqr root3/3? Is that height of pole? That doesn't seem right to me?
17- 17√3/3 = appr 7.18 m , why is it not reasonable
Thank you greatly! I got to your answer now understand
Tan30 = h1/17,
h1 = 9.81 m.
Tan45 = (h1+h2)/17 = (9.81+h2)/17,
9.81 + h2 = 17,
h2 = 7.2 m. = Ht. of pole.
To solve this problem, we can start by drawing a diagram.
Here's a representation of the situation described:
```
|\
| \ h
| \
| \
| \
-----|-----\
17m |
x
```
In this diagram, the tall building is represented by a vertical line, and the pole is represented by another line starting from the bottom of the building. The length of the pole is marked as 'h', and the distance from the observer to the building is marked as 17m.
We need to find the height of the pole, 'h'.
Let's analyze our diagram and use some trigonometry.
From the right triangle formed by the observer, the base of the pole, and the distance between them (17m), we can use the tangent function to find 'x', the height of the pole from the base:
tan(30°) = x / 17
Next, let's consider the right triangle formed by the observer, the top of the pole, and the distance between them (17m + x). We can use the tangent function again to find 'h', the height of the pole:
tan(45°) = h / (17 + x)
Now, let's solve these two equations simultaneously to find 'x' and 'h'.
We can start by finding 'x' using the first equation:
x = 17 * tan(30°) = 17 * 0.57735 ≈ 9.809
Now, let's substitute this value of 'x' into the second equation to find 'h':
tan(45°) = h / (17 + 9.809)
By rearranging the equation, we have:
h = (17 + 9.809) * tan(45°) ≈ 26.809 * 1 ≈ 26.809
Therefore, the height of the pole is approximately 26.8 meters to the nearest tenth.