2024年3月20日发(作者：)

Step 1:

Step 3：

Step 2：

In △ACD，

∠A ＝ 40°

GAC004 AE2 Project2

On measuring

AB ＝ 2.01m

AC ＝ 3.38m

∵tan∠DBC ＝ AD/BD

∠DBC ＝ 75.0719…°

Dede Song

∴tan∠DBC ＝﹙sin40°×3.38﹚÷﹙cos40°×3.38－2.01﹚

Using the ratios calculate the obtuse angle ∠CBA.

∵BD ＝ AD－AB ∴BD ＝ cos40°×3.38－2.01

∵cosA ＝ AD÷CA ∴cos40°＝ AD÷3.38 AD ＝ cos40°×3.38

∵sin A ＝ CD÷AC ∴sin40°＝ CD÷3.38 CD ＝sin40°× 3.38

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Let AD⊥CD, ∠D is a right angle.

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same.

Step 5:

Step 4:

In △ABC,

∴∠DBC ≈75°

GAC004 AE2 Project2

＝105°

On measuring：

∠CBA ＝105°

∠CBA ＝180°－75°

∵∠CBA +∠DBC =180°

∴∠CBA ＝180°－∠DBC

In △ABC,

According to the Sine Rule,

AC÷ sinB ＝ CB÷ sinA

∴ 3.38÷sin105° ＝ CB÷sin40°

∵ The area of △ABC ＝ ½. A

Dede Song

∴The results of the calculation and measurement are almost the same.

∴ The length of the CB after calculation and measurement are almost the

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CB ＝ 3.38×sin40°÷sin105°

CB ＝ 2.2492…m

≈ 2.25m

On measuring:

CB ＝ 2.25m

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Step 8:

Step 6:

Step 7：

In △ABC,

On measuring:

BD ＝ 1.3m

GAC004 AE2 Project2

On measuring

AB ＝ 2.24m

AC ＝ 2.21m

BC ＝ 2.01m

∴ S△ABC ＝ ½×1.3×3.38

In △ABC,

According to the Cosine Rule,

＝ 2.1834…㎡ ≈ 2.2㎡

＝ 2.197㎡≈ 2.2㎡

∵ cosA ＝﹙AC²＋AB²－BC²﹚÷﹙2×AC×AB﹚

Dede Song

∴ The area of △ABC in step⑤ and step⑥ are almost the same.

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∵ The area of △ABC ＝ ½.

∴ S△ABC ＝ ½×2.01×3.38×sin40°

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≈ 62 °

∠B ＝ 62°

≈ 54°

＝ 431／728

＝ 1739／3752

＝﹙2.24²﹢2.01²－2.21²﹚÷﹙2×2.01×2.24﹚

∠A ＝ 54°

Dede Song

＝﹙2.21²＋2.24²－2.01²﹚÷﹙2×2.21×2.24﹚

∴ The results of the calculation and measurement are almost the same.

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∠C ＝ 64°

GAC004 AE2 Project2

∴ ∠B ＝ 62.3877…°

∴ ∠A ＝ 53.6985…°

＝ 180°－54°－62°

＝ 64°

On measuring:

∴ ∠C ＝ 180°－∠A－∠B

∵ cosB ＝﹙AB²﹢BC²－AC²﹚÷﹙2×BC×AB﹚

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Step 9：

GAC004 AE2 Project2

Dede Song

∴The spreadsheet results, measurement results and calculation results are

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GAC004 AE2 Project2

almost the same.

40°

90°

Dede Song

Appendix

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35°

105°

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GAC004 AE2 Project2 Dede Song

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64°

54°

62°

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