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DerKrebs [107]
3 years ago
6

A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E. The captain then turns the boat 90° and travels

another 15 miles in the direction S 47° E. At that time, how far is the boat from the harbor entrance, and what is the bearing of the boat from the harbor entrance?
Mathematics
1 answer:
Serga [27]3 years ago
3 0

Answer:

Step-by-step explanation:

A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.

Displacement in vector form

= 28 cos43 i + 28sin43j

= 20.47 i + 19.1 j

The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E

Displacement

= 15 cos47 i - 15 sin47 j

= 10.22 i - 10.97 j

Total displacement

= 20.47 i + 19.1 j + 10.22 i - 10.97 j

= 30.69 i - 8.13 j

Magnitude of displacement

= 31.75 miles

Angle with east direction

TanФ = - 8.13 / 30.69

Ф = 15 degree  south of east.

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Dilation is the process in which the dimensions of a given shape is increased or decreased by a scale factor. Therefore the answers to the questions are:

A. Since the dilation of triangle XYZ do not affect the measure of its internal angles, then the trigonometric ratios of respective internal angles are the same.

B. segment CB = 10

ii. segment AB = 11.18

From the given information in the question, triangle XYZ is an image of triangle ACB. In triangle XYZ, given that Sin X = ; it implies that its hypotenuse is 5.59, and the opposite side as 5. So that;

Sin X =

X =  0.8945

X  =

Thus,

<X + <Y + <Z =

+  + <Z =

<Z =  -

   =

<Z =

So then, the third side can be determined by applying the Pythagoras theorem.

=  +

=  +

=  -

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x =

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x = 2.5

Thus,

Cos X =

          =

Cos X =

Tan X =

         =

Tan X =

Therefore:

A. Considering triangles XYZ and ACB, the measure of their respective internal angles are the same.

i.e <X ≅ <A

   <B ≅ <Z

   <C ≅ <Y

So that the trigonometric ratios of respective internal angles are the same.

B. Given that triangle XYZ was dilated by a scale factor of 2, then the respective length of each sides of triangle ACB is twice that of XYZ.

Then,

i. segment CB = 2 x segment YZ

                    = 2 x 5

segment CB = 10

ii. segment AB = 2 x segment XZ

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Hello!

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