Question

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 ∠B = 105° and ∠C = 20°, what is the distance, to the nearest tenth of a mile, between locations A and B?

Answer 1

We will first calculate ∠A:
∠∠A = 180° - ( 105° + 20 ° ) = 180° - 125° = 55°
Then we will use the Sine Law:
15 / sin 55° = AB / sin 20°
15 / 0.81915 = AB / 0.342
AB · 0.81915 = 15 · 0.342
AB · 0.81915 = 5.13
AB = 5.13 : 0.81915
AB = 6.26 ≈ 6.3 miles
Answer: The distance between the locations A and B is 6.3 miles.

Answer 2

Answer:

Distance between A and B is 5.7 miles

Step-by-step explanation:

In the given triangle ABC

∠B = 105° and ∠C = 20°

and distance between locations B and C = 15 miles.

We have to determine the distance between locations A and B.

In triangle ABC

∠A = 180 - (∠B + ∠C) = 180 - (105 + 20) = 180 - 125 = 55°

$\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$

Now we place the values of angles and distance BC in the formula

$\frac{sinA}{a}=\frac{sinC}{c}$

$\frac{sin55}{15}=\frac{sin20}{c}$

$\frac{0.8192}{15}=\frac{0.342}{c}$

$\frac{0.342}{c}=.0546$

$c=\frac{0.342}{.0546}=6.26$

Therefore distance between locations A and B is 6.3 miles