# Euclid 5

Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.

Result

b =  7.14 cm
c =  10 cm

#### Solution:

$c = c_1 +c_2 \ \\ c_1^2 = a^2 -v^2 \ \\ c_1 = \sqrt{ 7^2 - 5^2 } = 4.9 \ cm \ \\ v^2 = c_1 c_2 \ \\ c_2 = v^2/c_1 = 5^2 / 4.9 = 5.1 \ cm \ \\ \ \\ c = c_1 + c_2 = 10 \ \text{cm} \ \\ \ \\ c^2 = a^2+b^2 \ \\ b = \sqrt{ c^2 - a^2 } = 7.14 \ cm$

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