# Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.

Result

a =  11.54 m
b =  17.3 m
c =  20.8 m

#### Solution:

$c_b^2 = b^2 - v^2 \ \\ c_b = \sqrt{ 17.3^2 - 9.6^2 } = 14.39 \ \\ \ \\ v^2 = c_a c_b \ \\ c_a = v^2/ c_b = 9.6 / 14.39 = 6.4 \ m \ \\ \ \\ c = c_a + c_b = 20.8 \ \text{m} \ \\ \ \\ a^2+b^2 = c^2 \ \\ a = \sqrt{ c^2 - b^2} = \sqrt{ 20.8 \ \text{m}^2 - 17.3^2} = 11.54 \ m \ \\ b= 17.3 \ m \ \\ c = 20.8 \ \text{m} \ \\$

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