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
You might be interested in
Answer: (a) Percentage of 25 year old men that are above 6 feet 2 inches is 11.5%.
(b) Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%.
Step-by-step explanation:
Given that,
Height (in inches) of a 25 year old man is a normal random variable with mean and variance
.
To find: (a) What percentage of 25 year old men are 6 feet, 2 inches tall
(b) What percentage of 25 year old men in the 6 footer club are over 6 feet. 5 inches.
Now,
(a) To calculate the percentage of men, we have to calculate the probability
P[Height of a 25 year old man is over 6 feet 2 inches]= P[X>]
P[X>74] = P[ >
]
= P[Z > 1.2]
= 1 - P[Z ≤ 1.2]
= 1 - Ф (1.2)
= 1 - 0.8849
= 0.1151
Thus, percentage of 25 year old men that are above 6 feet 2 inches is 11.5%.
(b) P[Height of 25 year old man is above 6 feet 5 inches gives that he is above 6 feet] = P[X,
- X,
]
P[X >
I X >
] = P[X > 77 I X > 72]
=
=
=
=
=
=
= 0.024
Thus, Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%.