SOLUTION: I'm not sure how to set this up. " A Cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On the top of each tower is a pigeon. The two pigeons fly off at t
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Question 237420: I'm not sure how to set this up. " A Cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On the top of each tower is a pigeon. The two pigeons fly off at the same time and at the same speed directly to some grain on the level straight road between the towers. The pigeons reach the grain at the same time. How far is the grain from the foot of the cathedral tower?"
I was thinking of using the Pythagorean Theorem formula but, I didn't know which numbers to use for which.
please help if you can.
I have to assume that the 250 foot distance is the distance along the ground from the base of the cathedral tower to the base of the church tower. Otherwise, this problem gets ludicrously complex.
So if the pigeons leave at the same time and fly at the same speed, they must fly the same distance. That means that there is a point on the ground along that 250 foot distance that is equidistant from a 200 foot tower and a 150 foot tower.
Let's call the distance from the base of the cathedral tower to the point where the pigeons meet . Now we have a right triangle with a leg that is 200 feet and a leg that is feet. That means that the hypotenuse squared is
On the other side of the picture, the distance from the meeting point to the church tower must be . Again we have a right triangle with legs 150 and , so the hypotenuse squared must be .
These two hypotenuses are the flight paths of the two pigeons that we decided earlier must be equal in length. So:
Just solve for which we very cleverly defined as the distance the problem asks you to discover.
You can put this solution on YOUR website! I'm not sure how to set this up.
" A Cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On the top of each tower is a pigeon. The two pigeons fly off at the same time and at the same speed directly to some grain on the level straight road between the towers. The pigeons reach the grain at the same time.
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How far is the grain from the foot of the cathedral tower?"
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Draw the picture. You have two right triangles.
The hypotenuse of each triangle is the distance from the top to the grain.
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Since the times and the speeds are the same for both pigeons,
you only need to compare the distance each must fly. In both
cases that is the hypotenuse of a right triangle
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Let the distance from the base of the church tower be "x".
Then the distance from the base of the cathedral to the grain is "250-x" ft
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150^2+x^2 = 200^2 + 250^2 - 500x + x^2
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500x = 200^2 + 250^2-150^2
x = [200^2 + 250^2 - 150^2]/500
x = 160 ft.
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250-x = 90 ft. (distance the grain is from the base of the cathedral)
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Cheers,
Stan H.
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