During a war, Country A led a massive assault on the beach of Country B. The beach is 6.4 miles long. At 5 AM, a ship was first spotted from either end of the beach. The angle made with the ship from one end of the beach was 47°. The angle made with the ship from the other end of the beach was 71°. Determine the distance from the ship to either end of the beach at the moment the ship was first spotted.

5.3 miles & 6.85 miles

Step-by-step explanation:

To solve this question, I would use the sine rule

a/Sine A = b/Sine B = c/Sine C

Making a rough sketch, I have a scalene triangle with angles 47° and 71°, by default, the third angle is 61°

Given that, from my rough sketch

Angle C = 62°

Angle B = 71°

Angle A = 47°

Side c = 6.4 miles

We're looking for dudes a and b, applying our formula, we have

a/Sine 47 = 6.4/Sine 62

a/0.7314 = 6.4/0.8829

a/0.7314 = 7.25

a = 7.25 * 0.7314

a = 5.3 miles

b/Sine 71 = 6.4/Sine 62

b/0.9455 = 6.4/0.8829

b/0.9455 = 7.25

b = 7.25 * 0.9455

b = 6.85 miles

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