**In the adjoining figure, ABC is a triangle in which ∠B = 45**°** and ∠C = 60**°**. If AD ⟂ BC and BC = 8 m, find the length of the altitude AD.**

**Answer :**

ABC

**∠**B = 45° and **∠**C = 60°

AD ⟂ BC and BC = 8 m

In right △ ABD

tan 45° = AD/BD

1 = AD/BD

AD = BD

In right △ ACD

tan 60° = AD/DC

√3 = AD/DC

⇒ DC = AD/√3

BD + DC = AD + AD/√3

BC = (√3AD + AD)/ √3

⇒ 8 = [AD (√3 + 1)]/ √3

AD = 8√3/(√3 + 1)

= 4 (3 – √3) m

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