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.

bigmac Dec 14, 2019

#1**+2 **

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 **

Guest Dec 14, 2019