Question

watch the video and then solve the problem given below
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a man who is 6 feet tall is standing 12 feet from the base of a lamppost. the mans shadow is 5 feet long. how tall is the lamppost?
the lamppost is \\(\square\\) feet tall.
(round to the nearest tenth as needed.)

Explanation:

Step1: Identify similar triangles

The two triangles (lamp - base - tip of shadow and man - base of man - tip of shadow) are similar, so their corresponding sides are proportional. Let \( h \) be the height of the lamppost. The base of the larger triangle is \( 12 + 5=17 \) feet, height is \( h \). The smaller triangle has base 5 feet, height 6 feet.

Step2: Set up proportion

Using similarity, \(\frac{h}{17}=\frac{6}{5}\).

Step3: Solve for \( h \)

Cross - multiply: \( 5h = 6\times17 \). Calculate \( 6\times17 = 102 \). Then \( h=\frac{102}{5}=20.4 \).

Answer:

20.4