Q1Single correct1 Mark4 Jan 2026

An archer, from the point A, is aiming at a target, placed on the top of a 56 feet tall tree. The base of the tree is at the point C. From the archer’s position, the angle of elevation to the target is 45 $^\circ$ from his eye level. The archer, facing the tree, moves backwards on the straight line joining the points A and C, to a new position at the point B. From the point B, the angle of elevation from his eye level to the target becomes 30 $^\circ$. How far did the archer move from A to B (in feet) if his eye level is at a height of 6 feet from the ground?

A

$50\sqrt{3}$

B

$56\sqrt{3}$

C

$50(\sqrt{3} - 1)$

D

$50\left(1-\frac{1}{\sqrt{3}}\right)$

E

$\frac{50}{\sqrt{3}}$