Question

PLEASE HELP!!!

Answer 1

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

$\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

(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:

$\implies \sf \dfrac{AC}{\sin 37^{\circ}}=\dfrac{34}{\sin 32^{\circ}}$

$\implies \sf AC=\dfrac{34\sin 37^{\circ}}{\sin 32^{\circ}}$

$\implies \sf AC=38.61288345...$

$\implies \sf AC=38.6\:miles\:(nearest\:tenth)$

Therefore, weather station A is 38.6 miles from the storm.

Learn more about the Sine Rule here:

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