Question

SHELTER A group of hikers is constructing a lean-to shelter. A side view of the simple structure can be represented using the figure to the right. If the hikers plan to suspend a platform (represented by BD) level to the ground 1.25 ft above the ground, find the total height of the structure AC using the rules of triangle proportionality.

Answer to the nearest foot.

Answer 1

The total height of the structure AC using the rules of triangle proportionality is equal to 5ft.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion. Thus by triangle proportionality we have;

(6 - 1.5)/6 = (AC - 1.25)/AC

4.5/6 = (AC - 1.25)/AC

6(AC - 1.25) = 4.5AC {cross multiplication}

6AC - 7.5 = 4.5AC

6AC - 4.5AC = 7.5 {collect like terms}

1.5AC = 7.5

AC = 7.5/1.5 {divide through by 1.5}

AC = 5

Therefore, the total height of the structure AC is calculated to be 5 feet.