Thank you for visiting The distance between two locations A and B is calculated using a third location C at a distance of 15 miles from location B If. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
First find ∠A: ∠A = 180°-(105°+20°) = 180°-125° = 55°
Make sure you know the Law of Sin (or Sin Law):
15/sin 55° = AB/sin 20°, then 15 / 0.81915 = AB/0.342
AB(0.81915) = 15(0.342)
AB(0.81915) = 5.13
AB = 5.13 : 0.81915 (ratio)
AB = 6.26 = 6.3 miles
Therefore, the distance between location A and location B is 6.3 miles.
Make sure you know the Law of Sin (or Sin Law):
15/sin 55° = AB/sin 20°, then 15 / 0.81915 = AB/0.342
AB(0.81915) = 15(0.342)
AB(0.81915) = 5.13
AB = 5.13 : 0.81915 (ratio)
AB = 6.26 = 6.3 miles
Therefore, the distance between location A and location B is 6.3 miles.
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Rewritten by : Jeany
The distance between the two locations A and B is option C, 6.3 miles.
What is Triangle?
A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
We have,
for a triangle ABC,
∠B = 105° and ∠C = 20°
BC = 15 miles
We have the sine rule for a triangle ABC,
a / sin A = b / sin B = c / sin C
where a, b and c are the sides opposite to angles A, B and C respectively.
Here, by angle sum property,
∠A = 180° - (105° + 20°)
= 180° - 125°
= 55°
BC / sin A = AB / sin C
15 / sin (55°) = AB / sin (20°)
15 / 0.819 = AB / 0.342
AB = (15 / 0.819) × (0.342)
= 6.262 miles ≈ 6.3 miles
Hence the distance between locations A and B is 6.3 miles.
To learn more about Triangles, click on the link given below :
https://brainly.com/question/12460919
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