A boat is heading towards a lighthouse, whose beacon-light is 131 feet above thewater. From point A, the boat's crew measures the angle of elevation to the beacon,
5°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 21°. Find the distance from point A to point B.
Round your answer to the nearest tenth of a foot if necessary.
Answers
Answer:
Step-by-step explanation:
Assuming a flat earth
initial measurement
tan5 = 131 / d₁
d₁ = 131/tan5 = 1,497.3368... ft
d₂ = 131/tan21 = 341.2666674...ft
distance from A to B
1497.3368 - 341.26666 = 1,156.1 ft
Rather daring to specify to the answer to the nearest tenth of a foot when no given measurement accuracy is even close to that same precision.
Final answer:
This is a trigonometry problem that can be solved by using the tangent function to find the distances from the boat to the lighthouse at two different angles of elevation, and then subtracting to find the distance travelled by the boat.
Explanation:
This question involves the concept of trigonometry, specifically inverse trigonometric functions. We can solve it by creating two right triangles and using the trigonometric function known as tangent. Due to the nature of the problem, we will consider the lighthouse as the opposite side while the distance from the boat to the lighthouse will serve as the adjacent side.
When the boat is at point A, we can write the following equation using the tangent of 5° - tan(5°) = 131/DistanceA. Solve this equation to find DistanceA.
Next, do the same when the boat is at point B. The equation for this scenario is - tan(21°) = 131/DistanceB. Resolve this equation to find DistanceB.
The distance from point A to B (which is what the question asks for) is just the difference between DistanceA and DistanceB. Make sure to take the absolute value to avoid a negative distance, and round the result to the nearest tenth of a foot if necessary.
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Related Questions
Please help ! Thanks
Suppose we have two bags with the numbers. Each bag has a total of 100 numbers. In the first bag there are 31 lucky numbers, in the second bag there are 18 lucky numbers. We want to add one more bag with 100 numbers to decrease the probability that a randomly selected number from a random bag is the lucky number. How many lucky numbers should be in the third bag?
Convert 4.274.27 toimproper fraction
An expression is shown below (x^4/3)(x^2/3)
Answers
60 girls.
x(x2 + 5) – 6(x2 + 5)
x2(x – 5) + 6(x – 5)
x2(x + 5) – 6(x + 5)
Answers
The answer choice which shows how to determine the factors of the expression by grouping is; Choice D; x²(x + 5) – 6(x + 5)
Factorisation by grouping
The given expression is; x³ + 5x² – 6x – 30.
The expression is tetranomial, hence, by grouping into 2 terms each; we have;
- (x³+ 5x²) (– 6x – 30)
Ultimately, upon factorisation of each subunit of the expression, we have;
- x²(x+5) -6(x+5)
Read more on factorisation by grouping;
Answer:
D
Step-by-step explanation:
group them first :
( x3+5x2) and ( -6x-30)
then simply by gcf ( greatest common factor) :
x2(x+5) and -6(x+5)
and just add them together:
x2(x+5)-6(x+5)
bonus :
it can be written as (x2-6)(x+5)
Answers
Answer:
68% of the incomes lie between $36,400 and $38,000.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $37,200
Standard Deviation, σ = $800
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Empirical rule:
- Almost all the data lies within three standard deviation of mean for a normally distributed data.
- About 68% of data lies within one standard deviation of mean.
- About 95% of data lies within two standard deviation of mean.
- About 99.7% of data lies within three standard deviation of mean.
Thus, 68% of data lies within one standard deviation.
Thus, 68% of the incomes lie between $36,400 and $38,000.
9
%.
Answers
The probability of choosing a captain that is a girl two days in a row is 9%
How to determine the probability?
The given parameters are:
Boys = 21
Girls = 9
The total number of students is
Total = 21 + 9
Total = 30
This means that the probability of selecting a girl is:
P(Girl) = 9/30
For two days, the required probability is
P = 9/30 * 9/30
Evaluate
P = 9%
Hence, the probability of choosing a captain that is a girl two days in a row is 9%
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Answer:9%
U already provided the answer. Anyways have a good day!!
Answers
Answer:
the partial derivatives are
fx =5/9
fy =(-13/18)
Step-by-step explanation:
defining the vector v (from (2,1) to (1,3))
v=(1,3)-(2,1) = (-1,2)
the unit vector will be
v'=(-1,2)/√5 = (-1/√5,2/√5)
the directional derivative is
fv(x,y) = fx*v'x + fy*v'y = fx*(-1/√5)+fy(2/√5) =-2/√5
then defining the vector u ( from (2, 1) toward the point (5, 5) )
u=(5,5)-(2,1) = (3,4)
the unit vector will be
u'=(3,4)/5 = (3/5,4/5)
the directional derivative is
fu(x,y) = fx*ux + fy*uy = fx*(3/5)+fy(4/5)=1
thus we have the set of linear equations
-fx/√5*+2*fy/√5 =(-2/√5) → -fx + 2*fy = -2
(3/5) fx+(4/5)*fy=1 → 3* fx+4*fy = 5
subtracting the first equation twice to the second
3*fx+4*fy -(- 2fx)*-4*fy = 5 -2*(-2)
5*fx=9
fx=5/9
thus from the first equation
-fx + 2*fy = -2
fy= fx/2 -1 = 5/18 -1 = -13/18
thus we have
fx =5/9
fy =(-13/18)
Answers
Answer:
294.84
should be correct, I used a calculator.
Happy I helped.