CAT 2023 Set-3 | Quantitative Aptitude | Question: 17

Question

Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $B$ on $A C$. If $A D$ and $B E$ intersect at $O$ such that $\angle A O B=105^{\circ}$, then $\frac{A D}{B E}$ equals

• A. $\sin 15^{\circ}$
• B. $\cos 15^{\circ}$
• C. $2 \cos 15^{\circ}$
• D. $2 \sin 15^{\circ}$

   

Comments

Make a diagram and use exterior angle property, opposite angle theorem to find out some missing angles.

after wards in the $2$ Right angled triangles i used $base=hypotenuse*cos\theta$ and $height=hpyotenuse*sin\theta$ , where $\theta$ is the anlge between hypotenuse and base.

Finally i got $\frac{sin75^{\circ}}{sin30^{\circ}}$ I had to take help from chatgpt after this basically there is an identity that $sin\theta=cos(90-\theta)$ and $sin30^{\circ}=\frac{1}{2}$

Hence answer is $2*cos15^{\circ}$