Question

A boat sails on a bearing of 63 for 124 miles and then turns and sails 201 miles on a bearing of 192. Find the distance of the boat from its starting point.

Answer 1

The distance of the boat from its starting point is 156.226 .

According to the question

A boat sails on a bearing of 63 degree for 124 miles

i.e

By making 63 degree covers 124 miles

therefore ,

In figure below

AC = 124 miles

Then turns and sails 201 miles on a bearing of 192 degree

therefore ,

In figure below

CD = 201 miles  

Now,

According to the sum of triangle

∠ACB + ∠ABC + ∠BAC = 180°

∠ACB + 90° + 63° = 180°

∠ACB = 27°

CE = 180°  (Straight line )

therefore,

∠DCE = 192°  -  180°

          = 12°

As ∠C = 90°

therefore

∠ACD = ∠C - ∠DCE - ∠ACB

          = 90° - 12°- 27 °

          = 51°

Now,

The distance of the boat from its starting point = AD

By using Law of Cosines

As

The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.

The Law of Cosines (also called the Cosine Rule) says:

c² = a² + b² − 2ab cos(C)

As we have 2 sides and one angle available we can use   Law of Cosines

Therefore,

by substituting the value

(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)

(AD)² = (124)² + (201)² − 2*124*201 cos(51)

AD = 156.226

Hence, the distance of the boat from its starting point is 156.226 .

To know more about Law of Cosines here:

brainly.com/question/17289163

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