5.2.4 Applying Special Right Triangles (continued) Example 2
The 45 ° -45 ° -90 ° Triangle Theorem is used to determine the unknown lengths of the legs of a triangle in this application example. The hypotenuse is given to be 16 inches. To find the lengths of the sides of the square, which are the legs of a 45 ° -45 ° -90 ° triangle, set the hypotenuse equal to the unknown leg length times 2 , or 2 = 16. Solve for . Use a calculator to determine the approximate length of the side of the square to be 11 inches.
Example 3
The 30 ° -60 ° -90 ° Triangle Theorem describes the relationship between the lengths of the legs and hypotenuse in right triangles with angles 30 ° , 60 ° , and 90 ° . In these triangles, if the short leg is length s , the longer leg is length s 3 , and the hypotenuse is length 2 s . The 30 ° -60 ° -90 ° Triangle Theorem is used here to determine the unknown length of the hypotenuse and one leg of a triangle. The given triangle is a 30 ° -60 ° -90 ° triangle. The length of one leg is given as 8 units. Begin by expressing the unknown length of the short leg in terms of the known length of the longer leg. This yields a length for the shorter leg of 8 3/3. The length of the hypotenuse is 2 times the length of the shorter leg, or 16 3/3.
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