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In an isosceles triangle, the length of the base is 30, and the length of an altitude to one of the legs is 24.  Find the length of one of the legs.

 Dec 14, 2019
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Acute isosceles triangle.
Sides: a = 28.302 b = 28.302 c = 30

Area: T = 360
Perimeter: p = 86.604
Semiperimeter: s = 43.302

 

Angle ∠ A = α = 57.995° = 57°59'41″ = 1.012 rad
Angle ∠ B = β = 57.995° = 57°59'41″ = 1.012 rad
Angle ∠ C = γ = 64.011° = 64°39″ = 1.117 rad

 

Height: ha = 25.44
Height: hb = 25.44
Height: hc = 24


 From height h we calculate side a - Pythagorean theorem:
a^2 = h^2 + (c/2)^2, a = sqrt{ h^2 + (c/2)^2 } = sqrt{ 24^2 + (30/2)^2 } = 28.302 

 Dec 14, 2019

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