SOLUTION: 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

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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?
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
What we do is run what is known as a 'traverse' around to the second house and
calculate the distance back to the volcano. Let the volcano have coordinates at the origin (0,0).
Coordinates of house A:
x=15cos(230)=-9.64
y=15sin(230)=-11.49
Now, find the coordinates from house A to house B:
S40E is 140 degrees as an azimuth. An azimuth is an angle turned clockwise from north, or the y axis.
x=-9.64+14cos(140)=-20.36
y=-11.49+14sin(140)=-2.49
Now, use Pythagoras using these coordinates back to the volcano.
sqrt%28%28-20.36-0%29%5E2%2B%28-2.49-0%29%5E2%29=20.51
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.:):)