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Trigonometry questions about the sideview of an house

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This is a sideview of an house. We know that AF = 9 meters, AB = 6 meters and EF = 3 meters. Further we also know that ∠HED = 50° and ∠GBC = 50°.

a. Calculate DE

b. Show with a calculation that BD is around 6,5 meters

c. Calculate the entire height of the house.

Apr 18, 2019

#1
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a.

BH = 6m - 3m = 3m

DE = $$\dfrac{3\text m}{\sin\left(50^{\circ}\right)} \approx 3.92\text m$$

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Apr 18, 2019
#2
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b.

Construct line DP such that DP is perpendicular to HE and P is on line HE.

PE = $$\dfrac{3\text m}{\tan\left(50^{\circ}\right)} \approx 2.52\text m$$

BD = HE - PE = (9 - 2.52)m = 6.48m which is around 6.5 m.

Apr 18, 2019
#3
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c.

GD = $$\dfrac{\text{BD}}{2} \approx 3.24\text m$$

Entire height of the house is $$\text{GD} \tan\left(50^{\circ}\right) + 6\text m= 9.86\text m$$

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Apr 18, 2019