Answer:
38.6 miles
Step-by-step explanation:
The scenario has been modeled as a triangle, where A, B and C are the angles and a, b and c are the sides opposite the angles.
Side c
AB = 34 miles
Angle B
90° - 53° = 37°
Angle A
90° + 21° = 111°
Interior angles of a triangle sum to 180°
⇒ A + B + C = 180°
⇒ 111° + 37° + C = 180°
⇒ 148° + C = 180°
⇒ C = 180° - 148°
⇒ C = 32°
To find the measure of side b (AC), use the Sine Rule.
Sine Rule
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Substitute the values into the formula:
[tex]\implies \sf \dfrac{AC}{\sin 37^{\circ}}=\dfrac{34}{\sin 32^{\circ}}[/tex]
[tex]\implies \sf AC=\dfrac{34\sin 37^{\circ}}{\sin 32^{\circ}}[/tex]
[tex]\implies \sf AC=38.61288345...[/tex]
[tex]\implies \sf AC=38.6\:miles\:(nearest\:tenth)[/tex]
Therefore, weather station A is 38.6 miles from the storm.
Learn more about the Sine Rule here:
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