Question

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 streetlight? Give your answer to the nearest hundredth.

Answer 1

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