# Isosceles triangle 10

In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.

Correct result:

B =  41.41 °

#### Solution:

$a=c=\dfrac{ 2 }{ 3 } b \ \\ \cos B=\dfrac{ b/2 }{ a } \ \\ \cos B=\dfrac{ b/2 }{ \dfrac{ 2 }{ 3 } b } \ \\ \cos B=\dfrac{ 1/2 }{ \dfrac{ 2 }{ 3 } } \ \\ \ \\ B_{1}=\arccos(\dfrac{ 1/2 }{ 2/3 } ) \doteq 0.7227 \ \text{rad} \ \\ \ \\ B=B_{1} \rightarrow \ ^\circ =B_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =0.722734247813 \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =41.41 \ \ ^\circ =41.41 ^\circ =41^\circ 24'35"$

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