14.6 feet long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find the length of the cloth needed to make the tent, we can use the Pythagorean theorem.
The triangle formed by the tent is isosceles, the hypotenuse is equal to one of the equal sides, and we can use the Pythagorean theorem to solve for "x".
The length of the hypotenuse is:
√(1/2× 8)² + 6² )
√16 + 36 )
√52= 2√13
Since the tent is isosceles, the length of each of the two equal sides of the triangle is also "x", so we have:
2x = 2√13
Solving for "x", we get:
x = √13
Therefore, the length of the cloth needed to make the tent is:
2x + 8
= 2√13 + 8
= 14.61 feet
So the cloth would have to be 14.61 feet long.
Hence, 14.6 feet long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide.
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extension questions:
1) john wants to buy 10% more flooring than his room requires to account for errors. If boxes of flooring cover 20 square feet, how many boxes will john need in order to account for errors in measurement?
2) if hardwood flooring costs $3.98 per square foot, what will it cost john to put new floors in his living room?