MathDB
Ladders - AHSME 1982

Source:

January 19, 2006
geometrycongruent triangles

Problem Statement

In a narrow alley of width ww a ladder of length aa is placed with its foot at point PP between the walls. Resting against one wall at QQ, the distance kk above the ground makes a 45∘45^\circ angle with the ground. Resting against the other wall at RR, a distance hh above the ground, the ladder makes a 75∘75^\circ angle with the ground. The width ww is equal to
(A) a(B) RQ(C) k(D) h+k2(E) h\textbf {(A) } a \qquad \textbf {(B) } RQ \qquad \textbf {(C) } k \qquad \textbf {(D) } \frac{h+k}{2} \qquad \textbf {(E) } h
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