# 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.

Result

B =  41.41 °

#### Solution:

$a = c = \dfrac{ 2 }{ 3 } b \ \\ \cos B = \dfrac{ b/2 }{ a } \ \\ \cos B = \dfrac{ b/2 }{ \dfrac{ 2 }{ 3 } b } \ \\ \cos B = \dfrac{ 1/2 }{ \dfrac{ 2 }{ 3 } } \ \\ \ \\ B_{ 1 } = \arccos(\dfrac{ 1/2 }{ 2/3 } ) \doteq 0.7227 \ rad \ \\ \ \\ B = B_{ 1 } \rightarrow \ ^\circ = B_{ 1 } \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ = 41.4096221092 \ \ ^\circ = 41.41 ^\circ = 41^\circ 24'35"$

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