Question

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.

Answer 1

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.

Answer 2

The support given to the tent forms a right triangle.

The height of the tent is 5.3 ft

The given parameters are:

$\mathbf{Base = 6}$

$\mathbf{Hypotenuse= 8}$

The height is calculated as follows:

$\mathbf{Hypotenuse^2 = Base^2 + Height^2}$

Substitute known values

$\mathbf{8^2 = 6^2 + Height^2}$

This gives

$\mathbf{64 = 36 + Height^2}$

Collect like terms

$\mathbf{Height^2 = 64 - 36 }$

$\mathbf{Height^2 = 28 }$

Take square roots

$\mathbf{Height = 5.3 }$

Hence, the height of the tent is 5.3 ft

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