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? a. 42.4 miles b. 35.9 miles c. 6.3 miles d. 5.3 miles (how do you know what to do when C is given but you want values and the distance for A and B??)

Answer 1

To find the distance between locations A and B, use trigonometry and the law of sines. Angle A can be found by subtracting angles B and C from 180°. Then, use the law of sines to find the length of AB.

Step-by-step explanation:

To find the distance between locations A and B, we can use the concept of trigonometry and law of sines. Let's consider the triangle ABC. Angle B is given as 105° and angle C is given as 20°. Since the sum of angles in a triangle is 180°, we can find angle A by subtracting angles B and C from 180°. So, angle A = 180° - 105° - 20° = 55°.

Now, we can use the law of sines to find the length of AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In this case, we can use the ratio AB/sin(B) = BC/sin(A) to find AB. Plugging in the values, we get AB/sin(105°) = 15/sin(55°).

Solving this equation, we find AB ≈ 35.9 miles. So, the correct answer is (b) 35.9 miles.