Question

1. calculate the length of the diagonal of the state of wyoming.

write an equation you could use to find the length of the missing side of each right triangle. then find the missing length. round to the nearest tenth if necessary.
7 a = 48 yd; b = 55 yd

1. a = 23 in.; b = 18 in.
2. b = 5.1 m; c = 12.3 m

Explanation:

Step1: Apply Pythagorean theorem for Wyoming

The state of Wyoming forms a rectangle. The diagonal of the rectangle is the hypotenuse of a right - triangle with sides \(a = 275\) mi and \(b=365\) mi. The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So, \(c=\sqrt{a^{2}+b^{2}}=\sqrt{275^{2}+365^{2}}\).

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Step2: For right - triangle in question 7

The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(a = 48\) yd and \(b = 55\) yd.

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Step3: For right - triangle in question 8

Using the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), with \(a = 23\) in and \(b = 18\) in.

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Step4: For right - triangle in question 9

The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), we need to find \(a\). So, \(a=\sqrt{c^{2}-b^{2}}\), where \(b = 5.1\) m and \(c = 12.3\) m.

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Answer:

1. The length of the diagonal of Wyoming is approximately \(457.0\) mi.
2. Equation: \(c^{2}=48^{2}+55^{2}\), Missing length \(c = 73\) yd.
3. Equation: \(c^{2}=23^{2}+18^{2}\), Missing length \(c\approx29.2\) in.
4. Equation: \(a=\sqrt{12.3^{2}-5.1^{2}}\), Missing length \(a\approx11.2\) m.