Question

hi friends..
can anyone plz solve this question
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20 points ..
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Answer 1

AB = 12 cm

BC = 5 cm

AC = √(AB² + BC²)

AC = √(12² + 5²)

AC = √(144 + 25)

AC = √(169)

AC = 13 cm

BD = AB • BC / AC cm

BD = 12 • 5 / 13 cm

BD = 60/13 cm

AD = √(AB² - BD²)

AD = √(12² - (60/13)²)

AD = √(144 - (3600/169))

AD = √((24336 - 3600)/169)

AD = √(20736/169)

AD = 144/13 cm

Now,

cos ⟨DBC = BD/BC

cos ⟨DBC = (60/13)/5

cos ⟨DBC = (60/13) • (1/5)

cos ⟨DBC = 12/13

cot ⟨DBA = BD/AD

cot ⟨DBA = (60/13)/(144/13)

cot ⟨DBA = (60/13) • (13/144)

cot ⟨DBA = 60/144

cot ⟨DBA = 5/12

Hence found!

But there was no need for such a huge solution!

Since triangles ABC, ABD and BCD are congruent,

→ BD/BC = AD/AB = AB/AC = 12/13

→ BD/AD = CD/BD = BC/AB = 5/12

From these, we easily get,

=> cos ⟨DBC = 12/13

=> cot ⟨DBA = 5/12