Question

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point. A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees. Law of cosines: By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree. 30 degrees 39 degrees 46 degrees 50 degrees.

Answer 1

Law of cosine is applicable to all the triangles. The value of the angle by which the boat turns is 39.195°.

What is the law of cosine?

Law of cosine helps us to find the third side of the triangle when 2 sides and an angle are known. It is formulated as,

$c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}$

a, b, c is the sides of the triangle and,

$\gamma$ = angle opposite c

A.)

Given to us

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping.

When it stopped, the boat was 18 miles from its starting point.

According to the given statements, sides and angles can be written,

a = 25 miles

b = 28 miles

c = 18 miles

$\theta = x^o$

Substitute the values,

$c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}$

$18=\sqrt{25^{2}+28^{2}-2(25)(28) \cdot \cos \theta}\\\\\theta = 39.195^o$

Hence, the value of the angle by which the boat turns is 39.195°.

B.)

Given to us

Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock.

The angle between 25 miles and 28 miles is x degrees.

According to the given statements, sides and angles can be written,

a = 25 miles

b = 28 miles

c = 18 miles

$\theta = x^o$

Substitute the values,

$c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}$

$18=\sqrt{25^{2}+28^{2}-2(25)(28) \cdot \cos \theta}\\\\\theta = 39.195^o$

Hence, the value of the angle by which the boat turns is 39.195°.

Learn more about the Law of cosine:

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