Two docks are located on an east-west line 2581

ft apart. From dock A, the bearing of a coral reef is 58 degrees 28 prime
.
From dock B, the bearing of the coral reef is 328 degrees 28 prime
.
Find the distance from dock A to the coral reef.

Question

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Respuesta :

oeerivona oeerivona · Answer 1 · 2022-02-07T16:17:45+01:00

The line from dock A to dock B and the lines from the coral

reef to docks A and B form an isosceles triangle.

Correct response:

Given parameters are;

Distance between the docks = 2,581 ft.

Bearing of coral reef from dock A = 58°28'

Bearing of the coral reef from dock B = 328° 28'

Required:

The distance from dock A to the coral reef

Solution:

[tex]\theta _1 = 58^{\circ} 28' = \mathbf{\left(58 + \dfrac{28}{60} \right)^{\circ}} = 58.4\overline 6^{\circ}[/tex]

θ₂ = 328°28' = 328.4[tex]\overline 6[/tex]°

From the attached diagram, the angle at point C the coral reef is given as follows;

∠C = 180° - 2 × [tex]58.4\overline 6^{\circ}[/tex] = [tex]\mathbf{63.0\overline 6^{\circ}}[/tex]

According t the law of sines, we have;

[tex]\mathbf{\dfrac{AC}{sin \left(58.4\overline 6 ^{\circ}\right)}} = \dfrac{2,581}{sin \left(63.0\overline 6 ^{\circ}\right)}[/tex]

Which gives;

[tex]AC= sin \left(58.4\overline 6 ^{\circ}\right) \times \dfrac{2581}{sin \left(63.0\overline 6 ^{\circ}\right)} \approx \mathbf{2467.52}[/tex]

The distance from dock A to the coral reef, AC ≈ 2,467.52 feet

Learn more about the law of sines here:

https://brainly.com/question/512583