# Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17 m.

Result

a =  11.63 m
b =  17 m
c =  20.6 m

#### Solution:

$$\smash{ c_b^2 = b^2 - v^2 \\~\\c_b = \sqrt{ 17^2 - 9.6^2 } = 14.03 \\~\\ \\~\\v^2 = c_a c_b \\~\\c_a = v^2/ c_b = 9.6 / 14.03 = 6.57 \ m \\~\\ \\~\\c = c_a + c_b = 20.6 \ { m } \\~\\ \\~\\a^2+b^2 = c^2 \\~\\a = \sqrt{ c^2 - b^2} = \sqrt{ 20.6 \ { m } ^2 - 17^2} = 11.63 \ m \\~\\b= 17 \ m \\~\\c = 20.6 \ { m } }$$

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