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.

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

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

answer: 4 (:

step-by-step explanation: