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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The question is missing crucial information, such as the distances or angles from both weather stations to the storm, which makes it impossible to precisely determine the distance from weather station A to the storm.
This problem seems to be missing some essential information, such as the angles or distances from both weather stations A and B to the thunderstorm at point C, to establish a triangle and apply the Law of Cosines or the Pythagorean Theorem. Without these data, it is impossible to provide a definite answer to how far weather station A is from the storm.
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