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Find the inradius of triangle ABC if it's sides lengths are 29, 29, 40.

 


 

 Jan 29, 2022
 #1
avatar+1224 
+2

The inradius can be found using the formula A = rs, where A is the triangle's area, r is the inradius, and s is the triangle's semiperimeter.

 

\(s= \frac{29+29+40}{2} = 49\)

 

\(A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{(49)(20)(20)(9)} = 420\)

 

\(\rightarrow r = \frac{A}{s} = \frac{420}{49} = \boxed{\frac{60}{7}}\)

 Jan 29, 2022
 #2
avatar+13890 
+2

Find the inradius of triangle ABC if it's sides lengths are 29, 29, 40.

 

Hello Guest!

 

a = b = 29     c = 40

\(cos(\alpha)=\frac{c}{2\cdot b}=\frac{40}{2\cdot 29 }\\ \alpha =46.397^o\\ f(x)=tan( \frac{\alpha}{2})x\\ x=\frac{c}{2}=20\\ r=tan( \frac{\alpha}{2})\cdot x=tan(\frac{46.397^o}{2})\cdot 20 \)

\(r=8.\overline{571428}=\large \frac{60}{7}\)

laugh  !

 Jan 30, 2022

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