A surveyor is trying to find the length of a lake. He finds a baseline distance AB of 125 m. Angle A is measured to be 41.6° and angle B is measured at 124.3°. Find the length of the lake d. Please and Thank you.

Answers

Answer 1

Answer:

[tex]d = 340.7m[/tex]

Step-by-step explanation:

See attachment for question illustration

From the attachment, we have:

[tex]AB = 125m[/tex]

[tex]<A = 41.6[/tex]

[tex]<B = 124.3[/tex]

Required

Solve d

First, we need to calculate <C

[tex]<A + <B + <C = 180[/tex] --- angles in a triangle

[tex]41.6+ 124.3 + <C = 180[/tex]

[tex]165.9+ <C = 180[/tex]

Make <C the subject

[tex]<C = 180 - 165.9[/tex]

[tex]<C = 14.1[/tex]

Next, we apply Sine's law to solve for d

[tex]\frac{A}{Sin\ A} = \frac{B}{Sin\ B} =\frac{C}{Sin\ C}[/tex]

In this case:

[tex]\frac{d}{Sin\ 41.6} = \frac{125}{Sin\ 14.1}[/tex]

Make d the subject

[tex]d = \frac{125 * sin\ 41.6}{sin 14.1}[/tex]

[tex]d = \frac{125 * 0.66392621265}{0.24361501178}[/tex]

[tex]d = \frac{82.9907765812}{0.24361501178}[/tex]

[tex]d = 340.663639629[/tex]

[tex]d = 340.7m[/tex]

Hence, the base of the lake is approximately 340.7m

A Surveyor Is Trying To Find The Length Of A Lake. He Finds A Baseline Distance AB Of 125 M. Angle A

Related Questions

Laura bought some books. She spent a total of $71 after a discount of $5 off of her total purchase. Each book cost $4. How many books did she buy?


Answers

Answer:

4b-5=71

19 books

Step-by-step explanation:

b represents books, and 4 is the cost, so the cost (4•19) minus the discount (-5) equals 71 and solves the equation

Jada will draw two scale drawings of the same object on 1-cm grid paper. Each centimetre will represent a greater distance in the second
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Answers

Answer:

Jada is wrong. For example, say Jada is drawing scaled versions of a 10x10 yard square. In her first drawing, 1 centimeter = 1 yard, so the drawn square is 10x10 centimeters. In her second drawing, 1 centimeter = 2 yards, which is greater, like the problem says. This drawing will be only 5x5 centimeters, meaning the lengths will be smaller as each centimeter represents a greater number of yards.

Given that the triangles shown below are similar, what is the value of x?
D
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H
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O
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Answers

Answer:

the answer is D. 24

Step-by-step explanation:

the smaller triangle is half the size of the bigger triangle so just divide 48 by 2

Answer: D

Why?

Question tells you that both triangles are similar, but the obvious difference is that one is smaller than the other.

As u can see HA = PD
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By dividing the value of HM (which is 48) u can get the answer 24.

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1/4 off

Step-by-step explanation:

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What is an equation in point-slope form the line that passes through the point (-3,5) and (2,-3)?

Answer
Y-5=-8/5 (x+3)

Answers

Answer:

Y-5=-8/5 (x+3)

Step-by-step explanation:

Answer:

Y-5=-8/5 (x+3) good luck

How many 5/8 inch binder clips, laid side by side, make a length of 11 1/4 inches?

Answers

Answer:

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Step-by-step explanation:

Because 5/8×18 is 11 1/4

Answer:

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Step-by-step explanation:

Daniel plays two games in the casino. The first game he believes he has 60% chance to win. If he wins the first game, he will win the second game with 25% chance, if he loses the first game, he will win the second game with 75% chance. The winning prices for the first and second game are $1 and $2 respectively
A. What is the probability that he wins the second game?
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C. What is the expected value for the price he wins from the two games? What is the variance of it?

Answers

Answer:

1) the probability that he wins the second game is 0.45

2) the probability he wins the first game given that he won the second game is 0.333  

3) Expected Value is $ 1.5 and the variance is 0.75

Step-by-step explanation:

Given the data in the question;

Let Win1 represent first game victory

and Loss1 represent first game loss

Let Win2 denote second game victory

and Loss2 denote second game loss

now from the Tree diagram of Daniel;

P ( Win1 ) = 0.6

P ( Loss1 ) = 0.4

P ( Win2 | Win1 ) = 0.25

P ( Loss2 | Win1 ) = 0.75

P ( Win2 | Loss1 ) = 0.75

P ( Loss2 | Loss1 ) = 0.25

1) probability that he wins the second game will be;

P ( Win2 )  =  [P ( Win1 ) × P ( Win2 | Win1 )] + [P ( Loss1 ) × P ( Win2 | Loss1 ) ]

we substitute

= [0.6 × 0.25] + [0.4 * 0.75] = 0.45

Therefore the probability that he wins the second game is 0.45

2)

If he wins the second game, what is the probability that he also won the first game  will be;

{From Bayes' Theorem}

P ( Win1 | Win2 )  =  P ( Win1 ) × P ( Win2 | Win1 ) / P ( Win2 )

= 0.6 × 0.25 / 0.45 = 0.333  

Therefore the probability he wins the first game given that he won the second game is 0.333  

c)

winnings       probability

$0                  0.4 × 0.25 = 0.1

$1                   0.6 × 0.75 = 0.45

$2                  0.4 × 0.75 = 0.3

$3                  0.6 × 0.25 = 0.15

so Expected Value = ∑( winnings × individual win probability)

=  (0 × 0.1) + (1 × 0.45) + (2 × 0.3) + (3 × 0.15)

= 0 + 0.45 + 0.6 + 0.45

= $ 1.5

Variance = ∑( X² ) - (∑(X))²

∑( X² ) = Summation of ( Winnings² × Probability of Each Win )

so

Variance = 0 × 0 × 0.1 + 1 × 1 × 0.45 + 2 × 2 × 0.3 + 3 × 3 × 0.15 - ( 1.5 )²

Variance = 0 + 0.45 + 1.2 + 1.35 - 2.25

Variance = 3 - 2.25

Variance = 0.75

Therefore Expected Value is $ 1.5 and the variance is 0.75

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Step-by-step explanation:

Given that :

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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