Euclid3

Calculate the height and sides of the right triangle if one leg is a = 100 km and the section of hypotenuse adjacent to the second leg c_b = 14 km.

Final Answer:

b = 68.5586 km
c = 121.2447 km
h = 38.7482 km

a = 100 km c_{2} = 14 km a^{2} = c \cdot c_{1} b^{2} = c \cdot c_{2} c = a^{2} : c_{1} = b^{2} : c_{2} c = c_{1} + c_{2} a^{2} = c \cdot (c - c_{2}) a^{2} = x \cdot (x - c_{2}) 10 0^{2} = x \cdot (x - 14) - x^{2} + 14 x + 10000 = 0 x^{2} - 14 x - 10000 = 0 a = 1; b = - 14; c = - 10000 D = b^{2} - 4 a c = 1 4^{2} - 4 \cdot 1 \cdot (- 10000) = 40196 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 4 \pm 4 0 1 9 6}{2} = \frac{1 4 \pm 2 1 0 0 4 9}{2} x_{1, 2} = 7 \pm 100.244701 x_{1} = 107.244700608 x_{2} = - 93.244700608 c_{1} = x_{1} = 107.2447 ≐ 107.2447 km c = c_{1} + c_{2} = 107.2447 + 14 ≐ 121.2447 km b = c^{2} - a^{2} = 121.244 7^{2} - 10 0^{2} = 68.5586 km

h = c_{1} \cdot c_{2} = 107.2447 \cdot 14 ≐ 38.7482 km Verifying Solution: S_{1} = \frac{a \cdot b}{2} = \frac{1 0 0 \cdot 6 8 . 5 5 8 6}{2} ≐ 3427.9285 S_{2} = \frac{c \cdot h}{2} = \frac{1 2 1 . 2 4 4 7 \cdot 3 8 . 7 4 8 2}{2} ≐ 2349.0091 a_{2} = c \cdot c_{1} = 121.2447 \cdot 107.2447 ≐ 114.03 b_{2} = c \cdot c_{2} = 121.2447 \cdot 14 ≐ 41.1998 c_{3} = a^{2} + b^{2} = 10 0^{2} + 68.558 6^{2} ≐ 121.2447

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