Question

In a right isosceles triangle, the lengths of both legs are equal. For the given isosceles triangle, what is the value of x?

Answer 1

x = 6

Explanation:

sine law

a/ sin a = x / sin x

(72)^1/2 / sin 45º = x / sin 90

6 = x/1

multiply each side by 1

6 = x

Answer 2

well, we know the triangle besides being an isosceles, is also a right-triangle, so let's use the pythagorean theorem.

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{√(72)}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{x}\\ \end{cases}\implies (√(72))^2=x^2+x^2 \\\\\\ 72=2x^2\implies \cfrac{72}{2}=x^2\implies 36=x^2\implies √(36)=x\implies 6=x`