Question

Two weather stations are aware of a thunderstorm located at point C. The weather stations A and B are 27 miles apart. Triangle ABC with angle A N 34 degrees W and angle B at N 61 degrees W. How far is weather station A from the storm?

a) 14.7 miles
b) 23.7 miles
c) 28.8 miles
d) 49.3 miles

Answer 1

The distance from weather station A to the storm is 14.7 miles.

Step-by-step explanation:

To find the distance from weather station A to the storm, we can use trigonometry and the given angles. Since the distance between the two weather stations is 27 miles, we can treat this as the base of a triangle. Angle B (N 61 degrees W) is the angle formed by station B, the storm location, and station A. We can use the law of sines to find the distance from station A to the storm location:

To answer the question of how far weather station A is from the storm located at point C, we can use the law of sines in triangle ABC, with A and B being the weather stations, and C being the location of the thunderstorm. Given that station A and B are 27 miles apart, we need to find the distances from these points to the location of the storm, using the angles provided.

First, we establish the angle at point C (angle ACB). Since we are dealing with a triangle and the angles of a triangle sum up to 180 degrees, angle ACB = 180 - 34 - 61 = 85 degrees.
(27 miles) / sin(61 degrees) = x / sin(34 degrees)

Solving for x, we get x = (27 miles) * sin(34 degrees) / sin(61 degrees) = 14.7 miles.