By Semenov K.N.
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Additional resources for A basis of identities of the Lie algebra s(2) over a finite field
EXAMPLE 2 Verifying That a Triangle Is a Right Triangle Show that a triangle whose sides are of lengths 5, 12, and 13 is a right triangle. Identify the hypotenuse. Solution We square the lengths of the sides. 3 Geometry Essentials 31 Notice that the sum of the first two squares (25 and 144) equals the third square (169). Hence, the triangle is a right triangle. The longest side, 13, is the hypotenuse. See Figure 17. Figure 17 13 ᭹ 5 Now Work 90° PROBLEM 21 12 Applying the Pythagorean Theorem EXAMPLE 3 The tallest building in the world is Burj Khalifa in Dubai, United Arab Emirates, at 2717 feet and 160 floors.
For example, 1-4 is not a real number, because there is no real number whose square is -4. 2. The principal square root of 0 is 0, since 02 = 0. That is, 10 = 0. EXAMPLE 11 3. The principal square root of a positive number is positive. 4. If c Ú 0, then 11c22 = c. For example, 11222 = 2 and 11322 = 3. 4 ᭹ Examples 11(a) and (b) are examples of square roots of perfect squares, since 1 1 2 64 = 82 and = a b . 16 4 24 CHAPTER R Review Consider the expression 2a2. Since a2 Ú 0, the principal square root of a2 is defined whether a 7 0 or a 6 0.
5 (a) Show that a temperature of 97°F is unhealthy. (b) Show that a temperature of 100°F is not unhealthy. 153. * Express this distance as a whole number. 154. Height of Mt. Everest The height of Mt. * Express this height in scientific notation. 155. * Express this wavelength as a decimal. 156. * Express this diameter as a decimal. 157. † Express this diameter using scientific notation. 158. † Express this width using scientific notation. 159. Astronomy One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days).