Question

A city is planning an outdoor concert for an Independence Day celebration. To hold speakers and lights, a crew of technicians sets up a scaffold with two platforms by the stage. The first platform is 8 feet 2 inches off the ground. The second platform is 7 feet 6 inches above the first platform. The shadow of the first platform stretches 6 feet 5 inches across the ground. A technician is 5 feet 8 inches tall. The technician is standing on top of the second platform. Find the lengths of the shadow that is cast by the scaffold and the technician to the nearest inch.

Answer 1

The length of the shadow that is cast by the scaffold and the technician to the nearest inch is approximately 196 inches.

Solutions involving shapes with proportional relationships

Recall that where two triangles are said to be proportional, it means that their perimeters are similar.

Therefore, to solve this, first, we convert all figures into inches.

AC  = 8ft 2in. = 98in

CE = 7ft 6in = 90in

AB = 6ft 3in = 75in

Second,

Recall that the height of the technician = 5ft 8in. In inches that will be 68inches.

The height of the scaffold is arrived at by saying 188 + 68 = 256Inc

Recall that the triangles are proportional. Therefore, we say

$\frac{256}{98}$ = $\frac{s}{75}$

if we cross multiply we can then say

s = 75($\frac{256}{98}$)

s = 75 * 2.6122449

s = 195.918 or approximately 196 inches. Answer in Feet is 16ft 4in.


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