Two surveyors want to find the height of an electricity pylon - Leaving Cert Mathematics - Question 8 - 2012
Question 8
Two surveyors want to find the height of an electricity pylon. There is a fence around the pylon that they cannot cross for safety reasons. The ground is inclined at... show full transcript
Worked Solution & Example Answer:Two surveyors want to find the height of an electricity pylon - Leaving Cert Mathematics - Question 8 - 2012
Step 1
Explain how they could find the height of the pylon.
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Step 2
Write down possible values for the measurements taken, and use them to show how to find the height of the pylon.
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Step 3
Calculate the common length of the bars [AF] and [DE], in metres, correct to three decimal places.
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Step 4
In order to secure the bar [AF] to [DE], the manufacturer needs to know: - the measure of the angle EGF, and - the common distance |AG| = |DC|.
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To find the measures necessary for securing the bar [AF] to [DE]:
Calculate the Angle EGF:
From triangle AFB, we can find:
heta = an^{-1}(2) \ \
Price therefore angle EGF as:
ext{Angle EGF } = an^{-1}(2) \ ext{leads to} \
ext{Angle EGF} = 63.43° \ \
ext{to two decimal places } EGF ≈ 63.43°
\ \
2. **Calculate Distance |AG| = |DC|**:
Length found through basic distance measurement: \
$$ |AG| + |GE| = |GE| + |DC| \
|AG| ≈ 0.5m \
|DC| ≈ 1.7m ext{ based on distance included and horizontal bars.} $$
- Provide the distance: |AG| to the nearest decimal point as 0.558
- Lastly approximate length for anchoring at secured points to correct decimal places.
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