Question

Solve for x and then find the area of the figure .

Answer 1

Check the picture below.

`\bf \cfrac{44}{√(3)}=a\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{44}{√(3)}\cdot \cfrac{√(3)}{√(3)}=a}\implies \cfrac{44√(3)}{3}=a \\\\[-0.35em] ~\dotfill\\\\ x=\cfrac{a}{tan(24^o)}\implies x=\cfrac{(44√(3))/(3)}{tan(24^o)}\implies x\approx 57.057 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{A=\cfrac{1}{2}(x+44)(a)}\implies A\approx \cfrac{1}{2}(101.057)\left( (44√(3))/(3) \right)\implies A\approx 1283.596`