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Question

Given : $∠ A B C = 60^{\circ}$
$∠ D B C = 45^{\circ}$
and BC = 40 cm.Find the length of AD (in cm)

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Solution

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In $△ A B C$ ,
$tan 60 = \frac{A C}{B C}$
$\sqrt{3} = \frac{A C}{40}$
$A C = 40 \sqrt{3}$
In $△ B D C$ ,
$tan 45 = \frac{D C}{B C}$
$1 = \frac{D C}{40}$
$D C = 40$
$A D = A C - D C$
$A D = 40 \sqrt{3} - 40$
$A D = 29.28 c m$

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