Question

A submarine travels N45 W 16 miles. It then turns a course of 216 measured clockwise off of due north and travels until it is due west of its original position. How far is it from where it started?

Answer 1

19.5 miles

Explanation:

The question is represented in the image attached.

∠A = 45°, ∠B = 45° + (216° - 180°) = 81°

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

45° + 81° + ∠C = 180°

126 + ∠C = 180

∠C = 180 - 126

∠C = 54°

The sine rule states that for a triangle with sides a, b, c and their corresponding opposite angles A, B and C. The following rule holds:

`(a)/(sin(A))= (b)/(sin(B))= (c)/(sin(C))`

b = length of beginning of submarine to end point. Using sine rule:

`(b)/(sin(81)) =(16)/(sin(54)) \\\\b=(16)/(sin(54))*sin(81)\\\\b=19.5\ miles`