The angle of elevation of the top of a pillar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $h$ be the height of the pillar $PO$ and $O$ be the base of the pillar.In $	riangle POB$,$	an 30^\circ = \frac{h}{OB} \implies OB = h \cot 3

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) Let $h$ be the height of the pillar $PO$ and $O$ be the base of the pillar.In $	riangle POB$,$	an 30^\circ = \frac{h}{OB} \implies OB = h \cot 30^\circ = h\sqrt{3}$.In $	riangle POA$,$	an 15^\circ = \frac{h}{OA} \implies OA = h \cot 15^\circ$.We know that $\cot 15^\circ = \cot(45^\circ - 30^\circ) = \frac{\cot 45^\circ \cot 30^\circ + 1}{\cot 30^\circ - \cot 45^\circ} = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} = 2 + \sqrt{3}$.Given $AB = 40 \ m$,so $OA - OB = 40$.$h(2 + \sqrt{3}) - h\sqrt{3} = 40$.$h(2 + \sqrt{3} - \sqrt{3}) = 40$.$2h = 40 \implies h = 20 \ m$.

The angle of elevation of the top of a pillar at a point $A$ on the ground is $15^\circ$. On walking $40 \ m$ towards the pillar,the angle becomes $30^\circ$. The height of the pillar is $... \ m$.

Similar Questions

$AB$ is a vertical pole resting at the end $A$ on the level ground. $P$ is a point on the level ground such that $AP = 3 \, AB$. If $C$ is the mid-point of $AB$ and $CB$ subtends an angle $\beta$ at $P$,the value of $\tan \beta$ is

From the top of a lighthouse $60 \ m$ high with its base at the sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

$A$ person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is $45^\circ$. Which of the following statements is correct?

$A$ pole stands vertically inside a triangular park $ABC$. If the angle of elevation of the top of the pole from each corner of the park is the same,then in the $\Delta ABC$,the foot of the pole is at the

$A$ balloon is descending at a rate of $4 \, m/min$. Its angle of elevation from a point on the ground is $45^\circ$,which reduces to $30^\circ$ after $10 \, minutes$. At what distance from the observer will the balloon touch the ground?

Vedclass Test Series

Exam Paper Generator

Online Exam Module