Question : The length of the shadow of a vertical tower on level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. The height of the tower is:
Option 1: $10 \sqrt{3}$ m
Option 2: $5 \sqrt{3}$ m
Option 3: $5(\sqrt{3}+1)$ m
Option 4: $10(\sqrt{3}+1)$ m
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $5(\sqrt{3}+1)$ m
Solution : Let the height of the tower be $h$ meters. And $p$ is the shadow of the tower In $\triangle ABC$, ⇒ $\tan45^\circ = \frac{h}{p}$ ⇒ $p = h$....................................(equation i) In $\triangle ABD$ ⇒ $\tan30^\circ = \frac{h}{10+p}$ Putting the value $p$ from equation (i), we get: ⇒ $\frac{1}{\sqrt3} = \frac{h}{h+10}$ ⇒ $10 + h = \sqrt3h$ ⇒ $h(\sqrt3 - 1) = 10$ ⇒ $h = \frac{10}{(\sqrt3 - 1)}$ On rationalisation ⇒ $h = \frac{10(\sqrt3 + 1)}{(\sqrt3 - 1)(\sqrt3 + 1)}$ ⇒ $h = \frac{10(\sqrt3 + 1)}{2}$ ⇒ h= $5(\sqrt{3}+1)$ m Hence, the correct answer is $5(\sqrt{3}+1)$ m.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 metres longer than when it was 60°. The height of the tower is:
Question : If the length of the shadow of a vertical pole is $\sqrt{3}$ times the height of the pole, the angle of elevation of the sun is:
Question : If the angle of elevation of the sun decreases from $45^\circ$ to $30^\circ$, then the length of the shadow of a pillar increases by 60 m. The height of the pillar is:
Question : At 129 m away from the foot of a cliff on level ground, the angle of elevation of the top of the cliff is 30°. The height of this cliff is:
Question : The respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. What will be the angle of elevation of the top of the tower?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile