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.
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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