Pythagorean Worksheet PDF

Pythagorean Theorem A 90° angle is called a right angle. A right triangle is a triangle with a 90° angle. In a right triangle, the side opposite the 90° angle is called the hypotenuse and the remaining two sides are called the legs. The angles in any triangle add up to...

Pythagorean Theorem A 90° angle is called a right angle. A right triangle is a triangle with a 90° angle. In a right triangle, the side opposite the 90° angle is called the hypotenuse and the remaining two sides are called the legs. The angles in any triangle add up to 180°. In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side. Exercise 1. 1. Suppose that two angles in a triangle are 60° and 30°. Is it a right triangle? 2. Suppose that a triangle has a 100° angle. Is it a right triangle? Answer YES, NO, or MAYBE. 3. Suppose that a triangle has a 70° angle. Is it a right triangle? Answer YES, NO, or MAYBE. 4. Suppose the legs of a right triangle have lengths 3 and x, and the hypotenuse has length 5. Find x. 5. Suppose a triangle has sides of lengths 1, 3, and 2. Is it a right triangle?  Exercise 2. 1. The classical ladder problem, there is a building with a window 12 ft above ground level. You want to use a ladder to go up to the window. You decide to use good safe practice and use a 4:1 vertical to horizontal ratio. How long should the ladder be? 2. An algebraic problem, find out the length of sides A and B on the following triangle: C = 19 A =X B = 3X 3. An iterative problem, look at the following figure. Start by finding the value for X1, then for X2, then X3, and so on until you get the value for X6. Write the lengths as square roots, as that makes it simpler. What is the value of X6? 1 1 1 1 X3 X2 X4 1 X1 X5 1 1 X6 4. A word problem, grade is defined by rise over run. A 7% grade road would have a rise of 7ft for a run of 100ft. If a ramp is used to load a 3ft high truck bed, and that ramp has a grade of 25%, how long is the ramp in decimal feet? (nearest.01) Ex. 1 question 1, Yes 2, No 3, Maybe 4, 4 5, No | Ex. 2 question 1, 12.369 ft or 12’ 5” 2, X = 6.008; 3X = 18.025 3, X6 = 2.6457 4, 12.37ft