In a right triangle with base M, the second leg is unknown, and the hypotenuse is eight squared. Solve for M.
Answer (2)
In a right triangle with a hypotenuse of 64, we can express the base M in terms of the leg N using the Pythagorean theorem. The relationship is given by M = √(64 - N²). The value of M depends on the value of the unknown leg N.
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To solve for M in a right triangle where the base is M , the hypotenuse is given as 8, and the second leg is unknown, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b :
c 2 = a 2 + b 2
In this case, let's assign a = M (the base), b as the unknown side, and c = 8 (the hypotenuse). Plug these values into the equation:
8 2 = M 2 + b 2
Simplifying gives:
64 = M 2 + b 2
Since we are only asked to solve for M and the second leg is unknown, we can rearrange to express M 2 in terms of b 2 :
M 2 = 64 − b 2
From this equation, we see that the value of M depends on the value of b . Without the specific length for b , we can't calculate an exact numerical value for M . However, M can be found using this equation once b is known.
This method shows how the components of the Pythagorean Theorem interrelate in a right triangle and how solving for one side requires knowing the other two.
