Question : From the peak of a hill 300 m high, the angle of depression of two sides of a bridge lying on the ground are $45°$ and $30°$ (both ends of the bridge are on the same side of the hill). Then the length of the bridge is:
Option 1: $300(\sqrt3 - 1)$ m
Option 2: $300(\sqrt3 + 1)$ m
Option 3: $300\sqrt3$ m
Option 4: $\frac{300}{\sqrt3}$ m
Correct Answer: $300(\sqrt3 - 1)$ m
Solution : $AB$ = height of peak = 300 m $CD$ = length of Bridge We are given the angle of depression, i.e., $\angle EAC = 45°$ and $\angle EAD = 30°$ ⇒ $\angle ACB = 45°$ and $\angle ADB = 30°$ Now, \(In \triangle ABC\) \(\tan\theta = \frac{P}{B}\) \(\tan45 ^{\circ} =\frac{AB}{BC}\) \(1=\frac{AB}{BC}=AB:BC=1:1\) \(In\ \triangle ABD,\) ⇒ \(\tan30 ^{\circ} =\frac{AB}{BD}\) ⇒ \(\frac{1}{\sqrt{3}}=\frac{AB}{BD}\Rightarrow AB:BD=1:\sqrt{3}\) Now, \(CD = BD - BC\) ⇒ \(CD \Rightarrow \sqrt{3}-1\) $AB$ = 1 unit = 300 metre So, $CD=(\sqrt{3}-1)$ units = $300(\sqrt{3}-1)$ metres Hence, the correct answer is $300(\sqrt3 - 1)$ m.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : A pole of length 7 m is fixed vertically on the top of a tower. The angle of elevation of the top of the pole observed from a point on the ground is 60° and the angle of depression of the same point on the ground from the top of the tower is 45°. The height (in m) of
Question : From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?
Question : From the top of a lighthouse at a height of 20 metres above sea-level, the angle of depression of a ship is 30°. The distance of the ship from the foot of the lighthouse is:
Question : In a triangle$\frac{AB}{AC}=\frac{BD}{DC}$, $\angle$B = 70° and $\angle$C = 50°, then $\angle$BAD =?
Question : A person observes that the angle of elevation at the top of a pole of height 5 metres is 30°. Then the distance of the person from the pole is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile