This value is approximate.
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Explanation:
Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.
Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.
Based on those two interior angles, angle C must be...
A+B+C = 180
107+42+C = 180
149+C = 180
C = 180-149
C = 31
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To sum things up so far, we have these known properties of triangle ABC
Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).
b/sin(B) = c/sin(C)
b/sin(42) = 24/sin(31)
b = sin(42)*24/sin(31)
b = 31.1804803080182 which is approximate
b = 31.2 miles is the distance from the storm to station A
Make sure your calculator is in degree mode.
The weather station A is 31.2 miles from the storm
From the triangle shown:
m<B = 90° - 48°
m<B = 42°
m<A = 17° + 90°
m<A = 107°
m<A + m<B + m<C = 180° (Sum of angles in a triangle)
107° + 42° + m<C = 180°
m<C = 180° - 149°
m<C = 31°
The distance between the weather stations A and B = 24 miles
That is, AB = 24 miles
The storm is at point C
The length AC is found by using the rule of sines:
[tex]\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles[/tex]
The weather station A is 31.2 miles from the storm
Learn more on sine rule here: https://brainly.com/question/4372174
