Question

If either side of an isosceles triangle measures 24 inches and its base measures 16 inches, then what are its angles?

Answer 1

`A = cos^-1 frac{7}{9}, B = C = pi/2 - A/2`

Explanation:

`24 times 24 times 16 = AB times AC times BC`

we use "cos rule": `16^2 = 24^2 + 24^2 - 2 cdot 24 cdot 24 cdot cos A`

`frac{16^2 - 24^2 - 24^2}{- 2 cdot 24 cdot 24 } = cos A = -frac{(2^4)^2}{2 cdot (2^3)^2 cdot 3^2} + 1 = 1 - 2/9`

`A + B + C = pi ; B = C = x`

`A + 2x = pi Rightarrow x = frac{pi - A}{2}`