SECTION A.2 Geometry Essentials A15 Figure 14 5 12 13 905 l w h b Applying the Pythagorean Theorem The tallest building in the world is Burj Khalifa in Dubai, United Arab Emirates, at 2717 feet and 163 floors. The observation deck is 1483 feet above ground level. How far can a person standing on the observation deck see (with the aid of a telescope)? Use 3960 miles for the radius of Earth, and assume Earth is a sphere. Source: Council on Tall Buildings and Urban Habitat EXAMPLE 3 Solution From the center of Earth, draw two radii: one through Burj Khalifa and the other to the farthest point a person can see from the observation deck. See Figure 15. Apply the Pythagorean Theorem to the right triangle. Since 1 mile 5280 feet, 1483 feet 1483 5280 mile. = = Then d d d 3960 3960 1483 5280 3960 1483 5280 3960 2224.58 47.17 2 2 2 2 2 2 ( ) ( ) ( ) ( ) + = + = + − ≈ ≈ A person can see more than 47 miles from the observation deck. Notice that the sum of the first two squares 25 and 144 ( ) equals the third square 169 ( ) . That is, because 5 12 13 , 2 2 2 + = the triangle is a right triangle.The longest side, 13, is the hypotenuse. See Figure 14. Now Work problem 23 Figure 15 1483 ft 3960 mi d Now Work problem 55 2 Know Geometry Formulas Certain formulas from geometry are useful in solving algebra problems. For a rectangle of length l and width w , For a triangle with base b and altitude h , lw l w Area Perimeter 2 2 = = + bh Area 1 2 = FUN FACT Someone on the top floor observes the sun “set” about three minutes later than someone at the ground floor. j
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