Question

find the length x to the nearest whole number.
(round to the nearest whole number as needed.)

Explanation:

Step1: Use tangent function

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For the left - hand right - triangle with angle $44^{\circ}$, $\tan44^{\circ}=\frac{y}{540}$ (let the part of the height be $y$), so $y = 540\times\tan44^{\circ}$. For the right - hand right - triangle with angle $21^{\circ}$, $\tan21^{\circ}=\frac{z}{540}$ (let the other part of the height be $z$), so $z = 540\times\tan21^{\circ}$. And $x=y + z$.

Step2: Calculate $\tan44^{\circ}$ and $\tan21^{\circ}$ values

We know that $\tan44^{\circ}\approx0.9657$ and $\tan21^{\circ}\approx0.3839$.

Step3: Calculate $y$ and $z$

$y = 540\times0.9657=521.478$, $z = 540\times0.3839 = 207.306$.

Step4: Calculate $x$

$x=y + z=521.478+207.306=728.784\approx729$.

Answer:

$729$