Geometry word problem help?
Topic: The steps to problem solving
July 18, 2019 / By Shay Question:
An airplane lands at an airport 60 miles east and 25 miles north of where it took off. How far are the two airports
Can you guys explain to me how to solve this problem step by step?
Best Answers: Geometry word problem help?
Parris | 1 day ago
This is actually more of an algebra problem. For this, you have to picture a triangle. You're trying to find the hypotenuse of a right triangle, so you're going to use the Pythagorean theorem.
Picture the triangle with the right angle on the bottom right. The bottom left point is your starting destination. You're going to go 60 miles east, which is shown as right on a map, thus creating the bottom of the triangle. Then you're going to go 25 miles north, which is shown as up on a map. Thus creating the side. You have to set up an equation to solve for c, or the hypotenuse.
The Pythagorean theorem is a^2+b^2=c^2
If a is 60 and b is 25, then your equation will be set up as this: 60^2+25^2=c^2
Then you're going to simplify the left side of the equation, by first finding 60^2 and 25^2
You find that the equation is 3600+625=c^2
Then you simplify further and add 3600 and 625 together. That leaves your equation at 4225=c^2
Now, you think you may have found the answer, but you have one last step. You're trying to find c, not c^2. So you're going to find the square root of 4225, because the square root of c squared=c.
You find that you answer is c=65
That means your answer is 65 miles. The two airports are 65 miles apart.
Hope this helped!
👍 170 | 👎 1
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Originally Answered: Geometry Question, please help! Angles word problem?
*Adnan's answer is incorrect. If B = 135, then A = 3B = 3*135 = 405, and C = B/3 = 135/3 = 45. A + C = 405 + 45 = 450, which is not 180 or even a multiple of it.*
The first thing you want to do with this problem (which applies to these types of problems in general) is to describe it with equations or expressions wherever possible. There are a lot of key words for math operations that I'm sure are easy for you to recognize, but you're just not used to thinking of it that way. Every single piece of information in a word problem like that should be telling you something or helping you. As a general rule, you should be deriving at least 1 equation per sentence.
Here are a couple common words and their associated operations:
Division: fractional descriptions, e.g. "half of", "a third of", etc.
Addition: "more than"
Subtraction: "less than"
Also, whenever you see something like "x *IS* y", you should be thinking "equals".
"The measure of
So the airplane flew to an airport at an angle.
We can find the length of that by using Pythagorean Theorm.
C is our hypotenuse.
Let A be 60, and 25 be B, and C is how far.
65 miles away.
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It's a triangle the distance in between is the hypotenuse and the others are the legs. Square the legs (60 and 25) and add those answers together and then square root that to find your answer. Hope I helped!
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This problem is a basic case of the pythagrean theorem.
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Originally Answered: Could someone please explain this geometry problem to me?
Since there are no angles in that picture, I'm going to assume the path ABC is a straight path.
Then the combination of the angle that makes up ABD and DBC would be equal to 180 degrees.
Then you would get the following equation
2y + 6y - 12 = 180
8y - 12 = 180
8y = 192
y = 24
Now with y = 24, then DBC which is 6y - 12 = 6*24 - 12 = 72 - 12 = 60. And the units I used were degrees. You could use radians if you wanted and should get an equivalent (although numerically different) result in radians.