The Pythagorean Theorem in Three Dimensions Quick Check
The answers to the quick check are
1. 15.0 ft
2. 59.5 cm
3. 8.8 cm
4. 9.1 m
5. 92.9 cm
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To find the answers to the quick check for "The Pythagorean Theorem in Three Dimensions," you need to apply the Pythagorean theorem formula. Let's go through each question and explain how to find the answers:
1. For the first question, you probably have a right triangle in 3D with two sides given. You need to find the length of the hypotenuse. You can use the formula: c^2 = a^2 + b^2. Substitute the given values into the formula and solve for c. The answer should be 15.0 ft.
2. In the second question, you have another right triangle in 3D. You are given two side lengths and need to find the length of the third side. Use the Pythagorean theorem formula again (c^2 = a^2 + b^2), substitute the given values, and solve for c. The answer should be 59.5 cm.
3. The third question likely involves finding the length of a side in a right triangle where one side and the hypotenuse are given. Once again, use the Pythagorean theorem formula, but this time you will solve for the missing side a. The equation would be a^2 = c^2 - b^2. Substitute the given values and solve for a. The answer should be 8.8 cm.
4. In the fourth question, the objective might be finding the hypotenuse when two sides of a right triangle are given. Apply the Pythagorean theorem formula (c^2 = a^2 + b^2), substitute the given values, and solve for c. The answer should be 9.1 m.
5. Finally, the fifth question may involve finding the length of one side of a right triangle when both the hypotenuse and the other side are given. Use the Pythagorean theorem formula (a^2 = c^2 - b^2), substitute the given values, and solve for a. The answer should be 92.9 cm.
Remember that these explanations are general guidelines for solving questions related to the Pythagorean theorem in three dimensions. It's always essential to carefully read the question and correctly identify the sides of the right triangle before applying the formula.