Question 505417: A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 56 mi/h, how far is it from its starting position? Round your answer to 2 decimal places.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 56 mi/h, how far is it from its starting position? Round your answer to 2 decimal places.
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Draw this diagram:
From point A, draw a 56 mi horizontal line to point B
From point B, draw a 28 mi 45º northeast line to point C
Draw a line connecting point C to point A
You now have an obtuse triangle with AB=56 and BC=28 and their included angle ABC=135º
56=miles traveled for 1 hr at 56 mph
28=miles traveled for 1/2 hr at 56 mph
Using Law of cosine to solve:c^2=a^2+b^2-2abcosx
For given problem:
(AC)^2=(AB)^2+(BC)^2-AB*BC*cos135º
(AC)^2=56^2+28^2-56*28*cos135º
(AC)^2=3136+784-1568*cos135º=5028.74
AC=√(5028.74)=70.91 mi
ans:
At constant speed of 56 mi/hr, the car is 70.91 miles from its starting position
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