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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 chooses 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.

Respuesta :

Ashraf82

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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