A) The distance east from Pirates Cove of Captain Sparrow's ship when he drops the anchor is 45 miles
The distance south from Pirates Cove of Captain Sparrow's ship when he drops the anchor is 77.942 miles
B) The distance from Captain Sparrow's ship to Shipwreck Island is 67.693 miles
In the illustrative diagram,
C represents the Pirates Cove
S represents Captain Sparrow's ship when he drops the anchor
and I represent Shipwreck Island
N, E, W, and S represent the four cardinal points
First, we will determine the distance Captain Sparrow travels
Using the formula,
Distance = Speed × Time
∴ Distance = 30 miles/hour × 3 hours
Distance = 90 miles
This the distance Captain Sparrow covers when he drops the anchor
A)
The distance east from Pirates Cove of Captain Sparrow's ship when he drops the anchor is given by x
Using SOH CAH TOA
[tex]sin 30^\circ = \frac{x}{90}[/tex]
y = 90 × sin 30°
y = 45 miles
∴ The distance east from Pirates Cove of Captain Sparrow's ship when he drops the anchor is 45 miles
The distance south from Pirates Cove of Captain Sparrow's ship when he drops the anchor is given by y
Using SOH CAH TOA
[tex]cos 30^\circ = \frac{y}{90}[/tex]
y = 90 × cos 30°
y = 77.942 miles
∴ The distance south from Pirates Cove of Captain Sparrow's ship when he drops the anchor is 77.942 miles
B)
The distance from Captain Sparrow's ship to Shipwreck Island is given by /SI/
First, we will determine /CI/
By the Pythagorean theorem,
/CI/² = 80² + 20²
/CI/² = 6400 + 400
/CI/² = 6800
/CI/ = √6800
/CI/ = 82.4621 miles
Now, we will determine ∠ICA
Let angle ICA = θ
[tex]tan \theta = \frac{20}{80}[/tex]
tanθ = 0.25
θ = tan⁻¹ (0.25)
θ = 14.036°
∴ ∠SCI = 90° - (30° + 14.036°)
∠SCI = 90° - 44.036°
∠SCI = 45.964°
Now, consider Δ SCI
Using the laws of cosine
/SI/² = /SC/² + /CI/² - 2×/SC/×/CI/ cos(SCI)
/SI/² = 90² + 6800 - 2 × 90 × 82.4621 cos45.964°
/SI/² = 8100 + 6800 - 14843.178 cos45.964°
/SI/² = 14900 - 14843.178 cos45.964°
/SI/² = 14900 - 10317.6445
/SI/² = 4582.3555
/SI/ = √4582.3555
/SI/ = 67.693 miles
Hence, the distance from Captain Sparrow's ship to Shipwreck Island is 67.693 miles
Learn more on Trigonometry and Bearings & Distances here: https://brainly.com/question/22518031
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