# RT - inscribed circle

In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.

Result

r =  5 cm

#### Solution:

$a = 30 \ cm \ \\ b = 12.5 \ cm \ \\ \ \\ c = \sqrt{ a^2+b^2 } = \sqrt{ 30^2+12.5^2 } = \dfrac{ 65 }{ 2 } = 32.5 \ cm \ \\ \ \\ S = \dfrac{ a \cdot \ b }{ 2 } = \dfrac{ 30 \cdot \ 12.5 }{ 2 } = \dfrac{ 375 }{ 2 } = 187.5 \ cm^2 \ \\ s = (a+b+c)/2 = (30+12.5+32.5)/2 = \dfrac{ 75 }{ 2 } = 37.5 \ cm \ \\ \ \\ r = S/s = 187.5/37.5 = 5 = 5 \ \text { cm }$

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Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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