Example Question - hypotenuse calculation
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Calculation of Hypotenuse in a Right-Angled Triangle
The image portrays a right-angled triangle with one leg measuring 60 meters and the other leg measuring 80 meters. To find the length of the hypotenuse (`c`), we would use the Pythagorean theorem. The theorem states that in a right-angled 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 (the legs). The formula is: \[ c^2 = a^2 + b^2 \] where `a` and `b` are the lengths of the legs, and `c` is the length of the hypotenuse. Here, `a = 60 m` and `b = 80 m`, so we plug these values into the formula to get: \[ c^2 = (60)^2 + (80)^2 \] \[ c^2 = 3600 + 6400 \] \[ c^2 = 10000 \] To find `c`, we take the square root of both sides: \[ c = \sqrt{10000} \] \[ c = 100 \] Therefore, the length of the hypotenuse, `c`, is 100 meters. There is no need to round since the result is a whole number.
Calculation of Hypotenuse in a Right Triangle
题目描述了一个直角三角形ABC，其中∠BAC是直角，给出了AB的长度为3，AC的长度为2。由直角三角形的性质知，BC是三角形ABC的斜边。题目要求求出BC的长。 根据勾股定理（直角三角形的两条直角边的平方和等于斜边的平方），可以设BC的长为c，得到： AB² + AC² = BC² 3² + 2² = c² 9 + 4 = c² 13 = c² c = √13 所以BC的长度为√13。
Calculating Hypotenuse Using Pythagorean Theorem
The Pythagorean Theorem states that for a right-angled 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). This can be expressed as: \[ c^2 = a^2 + b^2 \] In the given triangle, the lengths of the two sides (a and b) are 4 and 8, respectively. Let's use this information to find the length of the hypotenuse (c): \[ c^2 = 4^2 + 8^2 \] \[ c^2 = 16 + 64 \] \[ c^2 = 80 \] Now we'll find the square root of both sides to solve for c: \[ c = \sqrt{80} \] The exact value of √80 can be simplified by factoring out squares from 80: \[ \sqrt{80} = \sqrt{16 \cdot 5} \] \[ \sqrt{80} = \sqrt{16} \cdot \sqrt{5} \] \[ \sqrt{80} = 4\sqrt{5} \] Therefore, the exact value of c is: \[ c = 4\sqrt{5} \]
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