construct triangle
ABC in which angle B = 60°, angle C = 45° and AB + BC + AC = 15
cm. Write the steps of construction,
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Answer:
∆ take 6 cm on scale name point A & B.
∆ taking point B draw a arc less than half of the line.
∆ make 60 angle. Draw a line where the arc intersect the point B arc.
draw ∆ abc with b= 60 & c=45.
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Tan60° = CD/AD
=> √3 = CD/AD
=> AD = CD/√3 ……….(1)
Tan45° = CD/DB
=> 1 = CD/DB
=> 1 = CD/(10-AD)
=> 10-AD = CD
=> AD = 10- CD ………(2)
=> By (1) & (2)
CD/ √3 = 10-CD
=> CD = 10√3 - √3CD
=> CD +√3CD = 10√3
= CD(1+√3) = 10√3
=> CD = 10√3 / (1+√3)
= CD = {10√3( 1-√3)} /{(1+√3)(1-√3)}
= CD = (10√3 - 30) / -2
=> CD = (30–10√3) / 2
=> CD = 15 - 5√3
=> CD = 15 - 5*1.732
=> CD = 15- 8.66
= CD = 6.36 cm ( approx)
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