Question : Let A and B be two towers with the same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of a and b are 30o and 45o, respectively. The ratio of the heights of A and B is:
Option 1: $1: 3$
Option 2: $1: \sqrt{3}$
Option 3: $\sqrt{3}: 1$
Option 4: $3: 1$
Correct Answer: $1: \sqrt{3}$
Solution : In $\triangle ACE$, $\frac{AC}{CE} = \tan 30^{\circ}$ ⇒ $\frac{AC}{CE} = \frac{1}{\sqrt3}$ ⇒ $CE = \sqrt3 AC$ -------------(i) In $\triangle BDE$, $\frac{BD}{ED} = \tan 45^{\circ}$ ⇒ $\frac{BD}{ED} = 1$ ⇒ $ED = BD$ -------------(ii) Since CE = ED, ⇒ $\sqrt 3 AC = BD$ ⇒ $\frac{AC}{BD} = \frac{1}{\sqrt3}$ So, the ratio of heights = $1: \sqrt3$ Hence, the correct answer is $1: \sqrt3$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : Let A and B be two towers with the same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 60°, respectively. The ratio of the heights of B and A is:
Question : Solve for $\theta: \cos ^2 \theta-\sin ^2 \theta=\frac{1}{2}, 0<\theta<90^{\circ}$.
Question : The difference between the semi-perimeter and the sides of ΔPQR are 18 cm, 17 cm, and 25 cm, respectively. Find the area of the triangle.
Question : The total surface area of a regular triangular pyramid with each edge of length 1 cm is:
Question : The sides $P Q$ and $P R$ of $\triangle P Q R$ are produced to points $S$ and $T$, respectively. The bisectors of $\angle S Q R$ and $\angle T R Q$ meet at $\mathrm{U}$. If $\angle \mathrm{QUR}=59^{\circ}$, then the measure of $\angle \mathrm{P}$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile