A quantity surveyor needs to find the total length of timber needed in order to make the triangular truss shown below. The length of [AC] is 6 metres, and the pitch of the roof is 35°, as shown. [AD] = [DE] = [EC] and |AF| = [FB] = [BG] = [GC]. (i) Calculate the length of [AB], in metres, correct to two decimal places. (ii) Calculate the total length of timber required to make the truss.

Leaving Cert Mathematics Trigonometry: A quantity surveyor needs to fin

A quantity surveyor needs to find the total length of timber needed in order to make the triangular truss shown below - Leaving Cert Mathematics - Question b - 2010

Question b

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A quantity surveyor needs to find the total length of timber needed in order to make the triangular truss shown below. The length of [AC] is 6 metres, and the pitch... show full transcript

Worked Solution & Example Answer:A quantity surveyor needs to find the total length of timber needed in order to make the triangular truss shown below - Leaving Cert Mathematics - Question b - 2010

Step 1

Calculate the length of [AB], in metres, correct to two decimal places.

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Answer

To find the length of [AB], we can use trigonometry. In triangle ABH:

The angle at A is 35°.
The length of AH can be determined as follows:

$|AH| = 3 ext{ m}$

Using the cosine function:

$ext{cos}(35^ ext{o}) = \frac{|AH|}{|AB|}$

Rearranging gives:

$|AB| = \frac{|AH|}{ ext{cos}(35^ ext{o})} = \frac{3}{ ext{cos}(35^ ext{o})} \approx 3.66 ext{ m}$

Thus, the length of [AB] is approximately 3.66 m, to two decimal places.

Step 2

Calculate the total length of timber required to make the truss.

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Answer

To find the total length of timber, we will calculate each segment:

Calculate |FD|:
$|FD| = \sqrt{1^2 + 2^2} imes 0.83 \times 2 imes \text{cos}(35^ ext{o}) \approx 1.352707 \text{ m}$
Calculate |BE|:
$|BE| = |AB| = 3.66 ext{ m}$
Calculate |BD|:
$|BD| = \sqrt{2^2 + (3.66)^2} \times ext{cos}(35^ ext{o}) \approx 5.430412 ext{ m}$

Finally, we sum these lengths:

Total length required = 6 + 2(3.66) + 2(1.63) + 2.325 = 20.296 ext{ m} \approx 20.30 ext{ m}.

A quantity surveyor needs to find the total length of timber needed in order to make the triangular truss shown below - Leaving Cert Mathematics - Question b - 2010

Worked Solution & Example Answer:A quantity surveyor needs to find the total length of timber needed in order to make the triangular truss shown below - Leaving Cert Mathematics - Question b - 2010

Calculate the length of [AB], in metres, correct to two decimal places.

Calculate the total length of timber required to make the truss.

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