Using the Pythagorean Theorem

Use the Pythagorean Theorem to solve problems 1, 2, 5, 7, and 8. For problems 1, 2, 5, 7, and 8, solve using the Pythagorean theorem. • Click the blinking dot next to each problem. Type in the numerical answer.• When entering your answers, do not include units or use variables (just type the numerical answer). • Decimal answers should be rounded to the nearest tenth; whole number answers should be written without a decimal point.(The instructions at the top of the page are to answer the riddle at the bottom of the page. You do not need to answer the riddle, the answers are just there to help you check your work.) 23.9 8.1 47.7 12 228 8 Look at problem #3 above. A student solved problem #3 incorrectly using the following method. a2 + b2= c2 0.92 + 1.22 = c2 0.81 + 1.44 = c2 2.25 = c2 c = 1.5Explain the student's error and give the correct answer. Look at problem #4 above. The Pythagorean theorem cannotbe used to solve problem #4.Why not? Look at problem #6 above. In this problem, we are asked to find the perimeter of each triangle. All of the triangles are right triangles because the contain a right angle. Since the distance between dots is 1 centimeter, triangle "c" has legs that are 3 cm and 5cm. We must use the Pythagorean theorem to find the length of the third side. First we square each leg to get 9 and 25, then we add those numbers to get 34. Next we take the square root, which gives us 5.8 (when rounded to the nearest tenth). To find the perimeter, we must add all three sides of the triangle together to get a sum of 13.8 centimeters. Look at problem #9 above. The lifeguard runs 90 feet along the beach at a speed of 15 ft the formula Time=Distance we can calculate that it took her 6 seconds to run this distance.She jumps into the water and swims to the drowning swimmer, as shown in the diagram. We can use the Pythagorean theorem to find the distance that she swims, because it is the hypotenuse of a right triangle with side lengths 30 feet and 40 feet. Using the Pythagorean theorem, we calculate that the distance is 50 feet.Since the lifeguard swims at a rate of 5 ft it takes her 10 seconds to swim that distance.Therefore, it takes a total of 16 seconds to reach the drowning swimmer.