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Question
Find the length of AD.
Given: ∠ABC = 60o.
∠DBC = 45o
and BC = 40 cm.
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Solution
From right triangle ABC,
tan 60° = `"AC"/"BC"`
⇒ `sqrt(3) = "AC"/40`
⇒ AC = `40sqrt(3)"cm"`
From right triangle BDC,
tan 45° = `"DC"/"BC"`
⇒ 1 = `"DC"/(40)`
⇒ DC = 40 cm
From the figure, it is clear that AD = AC - DC
⇒ AD = `40sqrt(3) - 40`
⇒ AD = `40(sqrt3 - 1)`
⇒ AD = 29.28 cm
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