The picture below shows a pole and its shadow: A pole is shown with a right triangle side. The right triangle has hypotenuse 221
cm and base 21 cm. What is the height of the pole?
1 answer:
The answer is 220cm
Explanation
The picture inserted is the Pythagorean Theorem, used to solve equations such as this. It works trying to find the length of any side in a right triangle.
Let's make the base of this triangle 'a' which we know is 21cm
While 'a' and 'b' in Pythagorean are interchangeable, 'c' will ALWAYS be the hypotenuse.
That being said, we also know that 'c' is 221cm
Once we plug in the numbers we have been given, our formula looks like this: 21 squared + b squared = 221 squared
Now it's time to square 'a' and 'c'
Our equation is now simplified to: 441 + b squared = 48841
Now, we need to isolate 'b squared' to find it's value. We do this by subtracting 441 from both sides (it needs to be from both sides to keep the equation even)
With 441 subtracted from both sides, our equation is now: b squared = 48400
Our last step is to find the square root of both sides of the equation, because 'b' is the value of the height of the triangle, but right now we have 'b squared' so to turn that into 'b' we have to find the square root of 'b squared', which would give us 'b' (square roots and squares cancel each other out).
We know that whatever we do to one side must also be done to the other, so since we just found the square root of 'b squared', now we need to find the square root of 48400, which is 220.
That would make our equation: b = 220
b = height = 220
Hope I helped!
Picture credit: Physics Classroom
Explanation
The picture inserted is the Pythagorean Theorem, used to solve equations such as this. It works trying to find the length of any side in a right triangle.
Let's make the base of this triangle 'a' which we know is 21cm
While 'a' and 'b' in Pythagorean are interchangeable, 'c' will ALWAYS be the hypotenuse.
That being said, we also know that 'c' is 221cm
Once we plug in the numbers we have been given, our formula looks like this: 21 squared + b squared = 221 squared
Now it's time to square 'a' and 'c'
Our equation is now simplified to: 441 + b squared = 48841
Now, we need to isolate 'b squared' to find it's value. We do this by subtracting 441 from both sides (it needs to be from both sides to keep the equation even)
With 441 subtracted from both sides, our equation is now: b squared = 48400
Our last step is to find the square root of both sides of the equation, because 'b' is the value of the height of the triangle, but right now we have 'b squared' so to turn that into 'b' we have to find the square root of 'b squared', which would give us 'b' (square roots and squares cancel each other out).
We know that whatever we do to one side must also be done to the other, so since we just found the square root of 'b squared', now we need to find the square root of 48400, which is 220.
That would make our equation: b = 220
b = height = 220
Hope I helped!
Picture credit: Physics Classroom
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