Randy wants to attach a 21 foot string of lights to the top of the 18 foot mast of his sailboat. How far from the base of the mast should he attach the end of the light string?​

Answer:

10.81665

Step-by-step explanation:

In order to solve this we can use pythagorean theorem, or [tex]a^{2} + b^{2} = c^{2}[/tex]

C represents the hypotenuse and a and b represent the two other sides.

We have the hypotenuse, 21 feet. We also have a side, 18 feet. We can plug these in and solve for a.

[tex]a^{2} + 18^{2} = 21^{2}[/tex]

[tex]a^{2} + 324 = 441[/tex]

Subtract 324 from both sides.

[tex]a^{2} =117[/tex]

Square root both side to remove the square.

[tex]\sqrt{a^{2} } =\sqrt{117}[/tex]

[tex]a=10.81665[/tex]

Hope this helps!

This  question is based on the Pythagorean theorem.  Therefore, 10.81665 feet  far from the base of the mast should he attach the end of the light string.

Given:

Randy wants to attach a 21 foot string of lights to the top of the 18 foot mast of his sailboat.

We need to determined the base of the mast should he attach the end of the light string.

According to the question,

By using Pythagorean theorem,

[tex]a^2 + b^2 = c^2[/tex]

Here, it is given that, b = 18 and c = 21.

Putting this value in above formula.

We get,

[tex]a^2 + 18^2 = 21^2[/tex]

[tex]a^2 = 441 - 324\\\\a^2 = 117[/tex]

Square root both sides. We get,

[tex]\sqrt{a^2} = \sqrt{117}[/tex]

a = 10.81665.

Therefore, 10.81665 feet  far from the base of the mast should he attach the end of the light string.

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