6 Directions: Find the leg of the hypotenuse to the nearest tenth.
7 Example 1 a2 + b2 = c2 Pythagorean Theorem Substitute for a and b. Find the length of each leg first.a2 + b2 = c2Pythagorean Theorem= c2Substitute for a and b.= c2Simplify powers.225 = cSolve for c; c = c2.15 = c
8 Example 2c45a2 + b2 = c2Pythagorean Theorem= c2Substitute for a and b.= c2Simplify powers.41 = c241 = cSolve for c; c = c2.6.4 c
9 Example 3 Pythagorean Theorem a2 + b2 = c2 Substitute for a and b. 57cPythagorean Theorema2 + b2 = c2Substitute for a and b.= c2Simplify powers.= c2Solve for c; c = c2.74 = c8.6 c
10 Example 4a2 + b2 = c2Pythagorean Theorem25b72 + b2 = 252Substitute for a and c.49 + b2 = 625Simplify powers.– –49Subtract 49 from each side.b2 = 5767Find the positive square rootb = 24
11 Example 5a2 + b2 = c2Pythagorean Theorem12b42 + b2 = 122Substitute for a and c.16 + b2 = 144Simplify powers.– –16Subtract 16 from both sides.4b2 = 128Find the positive square root.b 11.3
12 Directions: Determine whether or not the given numbers are possible measures for the sides of a right triangle.
15 Lesson SummaryUse the figure for Problems 1 and 2.1. Find the height h of the triangle.8 m2. Find the length of side c to the nearest meter.10 mch12 m3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers?6 m9 m2624 ≈ 51 ft