4. In the Old West, settlers made tents out of a piece of cloth thrown over a clothesline and then secured to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide?

Answers

Answer 1

Answer:

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.

What is Trigonometry?

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.

To learn more on trigonometry click:

brainly.com/question/25122835

#SPJ3

Answer 2

Answer: the cloth would have had to been 14.42 feet

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Virtually every time you try this stunt, the new triangles
are NOT similar.

Example:

Triangle A₀ . . . legs = 3 and 4; hypotenuse = √25 = 5 .
Triangle B₀ . . . legs = 6 and 8; hypotenuse = √100 = 10 .

Ratio of short legs = 6/3 = 2
Ratio of long legs = 8/4 = 2
Ratio of hypotenuses = 10/5 = 2
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Add 1 unit to all legs:

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Triangle B₁ . . . legs = 7 and 9; hypotenuse = √130

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Ratio of long legs = 9/5 = 1.8
Ratio of hypotenees = √(130/41) = 1.78 .

New triangles are NOT similar.

I think this ONLY works when the original triangles are
congruent, so the ratio of their similarity is 1:1.
When each leg of both triangles is extended by the same
amount, they are still congruent.

But the question stipulates that they are NOT congruent.
So the answer to the question is: No. Never.

They are similar, by SSS. This shows that the sides are all similar but may not be congruent. And they started out similar, and they have the same scale factor. If you had one more angle besides the 90, you would be able to figure out the angles inside and have AA to justify.
Sorry if this is a bad explanation.

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