3 Find the length of a hypotenuse EXAMPLE 1Find the length of a hypotenuseFind the length of the hypotenuse of the right triangle.SOLUTION(hypotenuse)2= (leg)2 + (leg)2Pythagorean Theoremx2 =Substitute.x2 =Multiply.x2 = 100Add.x = 10Find the positive square root.
4 GUIDED PRACTICEfor Example 11.Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.ANSWERLeg; 4
5 GUIDED PRACTICEfor Example 12.Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.hypotenuse; 213ANSWER
7 Standardized Test Practice EXAMPLE 2Standardized Test PracticeSOLUTION162 = 42 + x2Substitute.256 = 16 + x2Multiply.240 = x2Subtract 16 from each side.240 = xFind positive square root.≈ xApproximate with a calculator.ANSWERThe ladder is resting against the house at about 15.5 feet above the ground.The correct answer is D.
8 GUIDED PRACTICEfor Example 2The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder?3.about 23.8 ftANSWER
9 GUIDED PRACTICEfor Example 2The Pythagorean Theorem is only true for what type of triangle?4.right triangleANSWER
10 EXAMPLE 3Find the area of an isosceles triangleFind the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters.SOLUTIONSTEP 1Draw a sketch. By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles with the dimensions shown.
11 Find the area of an isosceles triangle EXAMPLE 3Find the area of an isosceles triangleUse the Pythagorean Theorem to find the height of the triangle.STEP 2c2 = a2 + b2Pythagorean Theorem132 = 52 + h2Substitute.169 = 25 + h2Multiply.144 = h2Subtract 25 from each side.12 = hFind the positive square root.
12 EXAMPLE 3Find the area of an isosceles triangleSTEP 3Find the area.12(base) (height)= (10) (12) = 60 m212Area =ANSWERThe area of the triangle is 60 square meters.
13 GUIDED PRACTICEfor Example 35.Find the area of the triangle.ANSWERabout ft2.
14 GUIDED PRACTICEfor Example 3Find the area of the triangle.6.ANSWER240 m2.
15 Find the length of the hypotenuse of the right triangle. EXAMPLE 4Find the length of a hypotenuse using two methodsFind the length of the hypotenuse of the right triangle.SOLUTIONMethod 1: Use a Pythagorean triple.A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 2, you get the lengths of the legs of this triangle: 5 2 = 10 and = 24. So, the length of the hypotenuse is = 26.
16 Method 2: Use the Pythagorean Theorem. EXAMPLE 4Find the length of a hypotenuse using two methodsSOLUTIONMethod 2: Use the Pythagorean Theorem.x2 =Pythagorean Theoremx2 =Multiply.x2 = 676Add.x = 26Find the positive square root.
17 GUIDED PRACTICEfor Example 4Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple.7.8.ANSWER15 in.ANSWER50 cm.
18 Daily Homework Quiz1.Find the length of the hypotenuse of the right triangle.ANSWER39
19 Daily Homework Quiz2.Find the area of the isosceles triangle.ANSWER1080 cm2
20 Daily Homework Quiz3.Find the unknown side length x. Write your answer in simplest radical form.ANSWER413