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Cooper and Drew are standing on the seashore 10 miles apart. The coastline is a straight line between them. Both can see the same ship in the water. The angle between the coastline and Cooper's view of the ship is 45 degrees. The angle between the coastline and Drew's view of the ship is 35 degrees. How far is the ship from Cooper?
A) 5.8 miles
B) 7.2 miles
C) 8.6 miles
D) 10 miles

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Answer:

Option A. 5.8 miles

Step-by-step explanation:

It is given in the question that angle SCD = 45°  and ∠ SAD = 35°

Distance between Cooper and Drew = 10 miles

Let distance between Ship and Cooper is = x miles

Now we apply Sine rule in the Δ SCD

[tex]\frac{sin100}{10}=\frac{sin35}{x}[/tex]

[tex]\frac{0.9848}{10}=\frac{0.5736}{x}[/tex]

By cross multiplication

(0.9848)x = 10(0.5736)

[tex]x=\frac{5.736}{0.9848}=5.82[/tex] miles

Option A. 5.8 miles is the correct option.

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