Question 49
In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If $$\angle BAC = 45^{\circ}$$ and $$\angle ABC=\theta\ $$, then $$\frac{AD}{BE}$$ equals
Solution
It is given, Angle BAE = 45 degrees
This implies AE = BE
Let AE = BE = x
In right-angled triangle ABD, it is given $$\angle ABC=\theta\ $$
$$\sin\theta=\frac{AD}{AB}\ $$
$$\sin\theta=\frac{AD}{x\sqrt{\ 2}}\ $$
$$\sqrt{\ 2}\sin\theta=\frac{AD}{BE}\ $$
The answer is option D.
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