Laura Bernett is 5 ft-4 inches tall. She stands 12 feet from a streetlight and casts a 5-foot-long shadow. How tall is the stree
tlight? Give your answer to the nearest hundredth.
1 answer:
Answer: the height of the streetlight is 19.47 feet
Step-by-step explanation:
The height of Laura Bernett is 5 ft-4 inches.
12 inches = 1 foot
4 inches = 4/12 = 1/3 foot
Therefore, her height is
5 + 1/3 = 16/3 foot
The diagram of the scenario is shown in the attached photo
The right angle triangle ABC and EBD formed are similar.
h represents the height of the streetlight
Total length of AB = 12 + 5 = 17 feet
Considering triangle BDE,
To determine the angle formed, θ, we would apply trigonometric ratio
Tan θ = opposite side/adjacent side
Tan θ = (16/3)/5 = 1.067
θ = 46.86 degrees
Considering triangle ABC,
Tan θ = h/AB
Tan 48.86 = h/17
h = 17tan48.86 = 17 × 1.145
h = 19.465
To the nearest hundredth,
h = 19.47 feet
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