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
