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A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent? An image shows the tent, the staked rope, and the measurements as a right triangle. The height of the triangle is unknown. The base of the triangle is 6 feet. The hypotenuse is 8 feet.

Respuesta :

To answer this you can use the Pythagorean Theorem. It states that a squared plus b squares equals c squared. C is the length of the hypotenuse and a and b are the other 2 sides. Please see the attached work to see how to answer this. The approximate height of the tent is 5.3 feet.
Ver imagen Mrscomputator
MrRoyal

The support given to the tent forms a right triangle.

The height of the tent is 5.3 ft

The given parameters are:

[tex]\mathbf{Base = 6}[/tex]

[tex]\mathbf{Hypotenuse= 8}[/tex]

The height is calculated as follows:

[tex]\mathbf{Hypotenuse^2 = Base^2 + Height^2}[/tex]

Substitute known values

[tex]\mathbf{8^2 = 6^2 + Height^2}[/tex]

This gives

[tex]\mathbf{64 = 36 + Height^2}[/tex]

Collect like terms

[tex]\mathbf{Height^2 = 64 - 36 }[/tex]

[tex]\mathbf{Height^2 = 28 }[/tex]

Take square roots

[tex]\mathbf{Height = 5.3 }[/tex]

Hence, the height of the tent is 5.3 ft

Read more about right triangles at:

https://brainly.com/question/6322314

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