You see that the shadow of a nearby 6-foot tall street sign is 3 feet 6 inches. You measure the shadow of the rock wall to be 22 feet 3 inches. What method can you use with this information to approximate the height of the rock wall? Approximate the height of the rock wall.

Question
Trigonometric Functions
asked 2021-03-01
You see that the shadow of a nearby 6-foot tall street sign is 3 feet 6 inches. You measure the shadow of the rock wall to be 22 feet 3 inches. What method can you use with this information to approximate the height of the rock wall? Approximate the height of the rock wall.

Answers (1)

2021-03-02
Since the shadows of the street sign and rock wall are created at the same time, the right triangles created by the heights and shadows must be similar since they are created by the same angle of elevation to the sun. If two triangles are similar, then their corresponding sides must be proportional. We can then use a proportion to approximate the height of the rock wall.
You are given that the street sign has a height of 6 ft and its shadow has a length of 3 ft 6 in. = 3.5 ft. You are also given that the rock wall has a shadow of 22 ft 3 in = 22.25 ft. Let hh be the height of the rock wall. Then:
height of street sign/length of steet=height of rock wall/length of rock
sign's shadow wall shadow
\(\displaystyle\frac{{6}}{{3.5}}=\frac{{h}}{{22.25}}\)
\(\displaystyle{22.25}{\left(\frac{{6}}{{3.5}}\right)}={h}\)
\(\displaystyle{38}≈\frac{{h}}{{22}}\)
The approximate height of the rock wall is then about 38 ft.
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