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Degger [83]
3 years ago
7

URGENT PLEASE ANSWER To find the distance across a river, a surveyor chooses points A and B on one side of the river. She then c

hooses a reference point C on the opposite side of the river and finds the following measurements:
AB=100 m∡A=47∘∡B=82∘
Find the distance from point A to point C. Enter just the numerical value of the answer - do not include "AC=" or any units - and round your answer to the nearest tenth.
Mathematics
1 answer:
Rus_ich [418]3 years ago
4 0

Answer:

The distance between A and C = 127.4

Step-by-step explanation:

* We have 3 different points A , B , C lets consider them as

 a vertices of a triangle ABC

- AB = 100

- m∠A = 47°

- m∠B = 82°

* To find the distance AC we can use the sin Rule

- In any triangle the ratio between the length of each side

 to the measure of each opposite angle are equal

- In Δ ABC ⇒ AB/sinC = BC/sinA = AC/sinB

* Lets do it to find the distance between A and C

∵ m∠A = 47° and m∠B = 82°

∵ The sum of the interior angles in any triangle is 180°

∴ m∠C = 180 - (47 + 82) = 180 - 129 = 51°

∵ AC/sin(82) = 100/sin(51)

∴ AC = 100 × sin(82) ÷ sin(51) = 127.423691

* AC = 127.4

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The distance by road from town A to town B is 257 km. What is 50% of that distance?
Marina86 [1]

Answer: 128.5km

Step-by-step explanation:

Since we are given the information that the distance by road from town A to town B is 257 km. To get 50% of the distance, we simply have to multiply the distance given by 50%. This will be:

= 50% × 257km

= 50/100 × 257km

= 0.5 × 257km

= 128.5km

Therefore, 50% of the distance is 128.5km.

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Solve this linear system 28x + 44y = 964.40 21x + 33y = 723.30
Sladkaya [172]

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Let's multiply the first equation by 4 and the second by -4

84x + 176y = 3857.6

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Add the equations together.

0 + 44y = 964.4

Simplify

44y = 964.4

Divide both sides by 44

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Since we have the value of y, let's plug 964.4/44 into y for the first equation.

28x + 44(964.4/44) = 964.40

Simplify the left side

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In conclusion,

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Check the picture below.

\bf (\stackrel{a}{1}~,~\stackrel{b}{-1})\qquad \impliedby \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c = \sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{1^2+(-1)^2}\implies c=\sqrt{2} \\\\[-0.35em] ~\dotfill

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