document.write( "Question 321320: on june 12, 1991, pyroclastic explosion in mt. pinatubo occured. residents of house A located 15km from the volcano in the direction of 230 degrees were asked to evacuate. Another house B is located 14km away from A in thw direction S 40 degrees E. is the house B in danger zone if it was necessary to evacuate everyone within the radius of 20km. from the volcano? \n" ); document.write( "

Algebra.Com's Answer #230161 by galactus(183) $\"\"$ $\"About$

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What we do is run what is known as a 'traverse' around to the second house and \r
\n" ); document.write( "\n" ); document.write( "calculate the distance back to the volcano. Let the volcano have coordinates at the origin (0,0).\r
\n" ); document.write( "\n" ); document.write( "Coordinates of house A:\r
\n" ); document.write( "\n" ); document.write( "x=15cos(230)=-9.64
\n" ); document.write( "y=15sin(230)=-11.49\r
\n" ); document.write( "\n" ); document.write( "Now, find the coordinates from house A to house B:\r
\n" ); document.write( "\n" ); document.write( "S40E is 140 degrees as an azimuth. An azimuth is an angle turned clockwise from north, or the y axis. \r
\n" ); document.write( "\n" ); document.write( "x=-9.64+14cos(140)=-20.36
\n" ); document.write( "y=-11.49+14sin(140)=-2.49\r
\n" ); document.write( "\n" ); document.write( "Now, use Pythagoras using these coordinates back to the volcano. \r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28%28-20.36-0%29%5E2%2B%28-2.49-0%29%5E2%29=20.51\"$ \r
\n" ); document.write( "\n" ); document.write( "They do not need to evacuate. They have 1/2 a mile to spare. Though, that is a close call for a volcano with a pyroclastic flow.:):)\r
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