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How do you find the third side of a right triangle if the base is x = 20m and height is y = 20m?

Answer
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Hint: Draw a rough diagram of a right-angle triangle ABC right angled at B. Now, assume the side BC as base and AB as height of the triangle. Apply the Pythagoras theorem given as: - base2 + perpendicular2 = hypotenuse2 and substitute the values of base and perpendicular as 20 each and calculate the value of hypotenuse to get the answer.

Complete answer:
Here, we are provided with a right-angle triangle with the length of its base equal to 20m and length of its height equal to 20m. We have to determine the third side, that is hypotenuse of this triangle.
Now, let us draw a diagram of the given situation. So, we have,
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In the above figure we have assumed a right-angle triangle ABC right angled at B. We have considered BC as the base whose length is x = 20m and AB as the height or perpendicular whose length is y = 20m. AC is the hypotenuse whose length is unknown.
Now, we know that we can apply the Pythagoras theorem in a right-angle triangle to determine the unknown side if the length of the other two sides are given. So, we have,
In ΔABC,
AB = y = 20m = perpendicular (height) = p
BC = x = 20m = base = b
Applying Pythagoras theorem given as: - p2+b2=h2, we have,
h2 = hypotenuse2
h2=AC2p2+b2=AC2AC2=AB2+BC2AC2=y2+x2AC2=(20)2+(20)2
AC2=2×(20)2
Taking square root both sides, we get,
AC=2×(20)2AC=202m
Hence, the length of the third side is 202m.

Note: One may note that besides Pythagoras theorem we can also apply the method of trigonometry to find the length of side AC. What we can do is we will first determine the angle C by using the formula: - tanC=yx=2020=1. Hence, angle C will be 45. Now, we will use the ratio sinC=yAC and by substituting the known value of y = 20 and sin45=12, we will get the value of AC. You may also use cosC=xAC as it will not alter the answer.