Assertion (A) : A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wal

Question

Assertion (A) : A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to which the ladder reaches is 8 m , then the length of the ladder is 10 m .\ Reason (R) : The ladder makes an angle of $60^{\circ}$ with the ground.\

Professor PC Thomas Classes · Answer

(c): Let $A B$ be the wall and $A C$ be the ladder\ ∴ Reaso ; false.\ In $	riangle A B C$, we have\ $(A C)^{2}=(A B)^{2}+(B C)^{2}$\ $=(8)^{2}+(6)^{2}=64+36=100$\ $\Rightarrow A C=10 \mathrm{~m}$\ Hence, length of the ladder is 10 m .\ So, assertion is true.\ Now, if ladder makes angle $60^{\circ}$ with ground, then\ $	an 60^{\circ}=\frac{A B}{B C}=\frac{8}{6}=\frac{4}{3} 
eq \sqrt{3}$\ $	herefore \quad$ Reason is false.\ Hence, assertion (A) is true and reason(R) is false.